merajnansabkaapna

Playing with Pascal's Triangle, part 1

2009-05-10T01:48:00.001-07:00

Playing with Pascal's Triangle, part 1,
originally uploaded by origami_madness.

wow

Triangle

2009-05-10T01:28:00.001-07:00

Triangle,
originally uploaded by Velo Steve.

mall about maths

माय पेंसिल work

2009-01-06T21:33:00.000-08:00

माय पेंसिल work

2009-01-06T21:31:00.000-08:00

माय पेंसिल work

2009-01-06T21:28:00.000-08:00

माय पेंसिल work

2009-01-06T21:25:00.000-08:00

wh3

2009-01-06T21:21:00.000-08:00

wh1

2009-01-06T21:19:00.000-08:00

whoooo

2009-01-06T21:17:00.000-08:00

पियूष constant

2008-11-29T23:46:00.000-08:00

AMAZING NUMBER NINE,(PIYUSH CONSTANT).
IT IS VERY INTERESTING ,IT IS MY OWN SEARCH,I LOVE MATHS,IN THE FUTURE VERY SOON MY OWN BOOK ON MATHS WILL PUBLISH MATHS--- A STUDY(IN HINDI),OR MAY BE IN THE FORM OF WEBSITE.
TAKE ANY NUMBER OF DIGITS,HERE I AM TAKING 25 AND 32,NOW
YOU CAN WRITE THEM IN FOUR WAYS LIKE THAT
25*32=800
25*23=575
52*23=1196
52*32=1664
NOW VERY AMAZING,SUBSTRACT BIGGER ONE TO ANY LOWER,ONE BY ONE
1664-1196=468=4+6+8=18=1+8=9
1664-575=1089=1+0+8+9=18=1+8=9
1164-800=864=8+6+4=18=1+8=9
1196-575=621=6+2+1=9
1196-800=396=3+6+9=18=1+8=9
800-575=225=2+2+5=9
ALWAYS NINE,FOR ANY DIGITS,NO BODY CAN COPY ALL RIGITS RESERVED TO PIYUSHDADRIWALA,IT IS JUST MY LOVEY BLOGGERS WHO HAVE INTEREST IN MATHS.LOVE TO ALL
PIYUSHDADRIWALA
www.piyush-g.741.com
www.piyushdadriwalamaths.co.in

2008-11-29T23:42:00.000-08:00

whoo

2008-08-26T07:21:00.001-07:00

http://www.myyearbook.com/piyushdadriwala

code

2008-07-05T02:40:00.000-07:00

code

2008-06-16T07:56:00.001-07:00

Rarest Items in the Worldtakes

2008-02-15T05:11:00.000-08:00

Rarest Items in the Worldtakes a peek inside the world of the uncommon and elusive. From wine, coins and jewels to, pets and food,mirror image book -- they reveal the world's rarest items

WORLD FIRST MIRROR IMAGE BOOK

takes a peek inside the world of the uncommon and elusive. From wine, coins and jewels to, pets and food -- they reveal the world's rarest items

Rarest Gems
The world's rarest gem is believed to be painite, a gem that most have never heard of. The painite is orangish or reddish brown and was first discovered in Burma in the '50s. Within the last couple of years, the source of the two original painite crystals was discovered and now a few hundred faceted stones exist. A more well-known (but still very rare) gem is the red diamond.

Rarest Signature
He may have done a lot of writing, but with only 6 of them in existence William Shakespeare's signature is one of the rarest of all and is valued somewhere around $3 million dollars.

Rarest Cats & Dogs
Of the rarest cat breeds, the Ashera (pic. left) is the most expensive ($20K+), the Sokoke the most exotic (from the wilds of Africa), and the Egyptian Mau has the coolest history (lived with the Egyptians). As for dog breeds, the one that keeps popping up on all the "rare" lists is the Lundehund, originally bred by the Vikings to hunt Puffins. Other rare breeds include Otterhounds and Stabyhounds.

Rarest Record Albums
In 1999, Mark David Chapman's copy of John Lennon and Yoko Ono's album Double Fantasy, autographed by Lennon five hours before Chapman fatally shot him, sold. The album had been found in a flower planter outside Lennon's home, at the scene of his murder. The record bears the forensically-certified fingerprints of Chapman, and was even used as evidence in the case against him. Price tag: $460,000. Or was it?

Rarest Stamps
According to Wikipedia, the most expensive item by weight and volume is the Treskilling Yellow stamp from Sweden. It has a current estimated worth of $2.3 million. Here's what makes it so valuable: In 1858, when the currency was known as the skilling, the 3-skilling stamp ("treskilling") was printed in blue. And an 8-skilling stamp was printed in yellow. But due to a printing error, a few 3-skilling stamps were printed in yellow.

Rarest Sea Salt
The earliest known sea salt produced by the Japanese may be the rarest of all. Called Amabito No Moshio ("Ancient Sea Salt"), unpolluted sea water is collected from the Seto-uchi inland sea, infused with seaweed to develop the "unami", and then processed by cooking in an iron kettle, put into a centrifuge, and finally, cooked over an open fire while stirring constantly. The salt is worth over $40 per pound.

Rarest Jeans
According to the Guinness Book of World Records, the most valuable jeans are an original pair of Levi Strauss & Co 501 jeans aged over 115 years old which were sold to a collector in Japan for $60,000 through eBay in 2005. Quite rare indeed considering a new pair sells for $46.

Rarest Baseball Cards
In February 2007, a "near mint-mint" Honus Wagner sold for $2.3 million, at that point probably the highest sale for a baseball card in history. Then, in September 2007, the same card was reportedly sold again. This time for $2.8 million to a private collector. The card in question, aT206 Honus Wagner, was made by the American Tobacco Company in 1909. It has been called the "Mona Lisa of baseball cards."

Rarest Comic Books
One of the rarest comic books still in existence in near-perfect condition is an issue of "Amazing Spider-Man #1," rare not only because of its singularity but also because of its quality. The comic book sold for only 12 cents per copy when it was published in March 1963, and is now worth over $40K -- not an exceedingly high price for comic books -- but extremely rare in such pristine condition.

Rarest Real Estate
At the intersection of location, exclusivity and history you find some of the rarest pieces of real estate. With that criteria, Luxist.com blogger's pick for the rarest piece of real estate currently on the market is Bran's castle, the castle in Transylvania that inspired Bram Stoker's Dracula, which is expected to fetch upwards of $135 million.

Rarest Horses
The Sorraia Horse is said to be the direct descendant of the wild Iberian horse but only 200 currently remain living in South Iberia. The Tiger Horse is a rare breed which is said to have existed in Ancient Spain and the beginning of the New World. Rare in terms of its abilities and characteristics, is the Lipizzaner (pic. left). Bred for its military prowess, one of these animals can sell for up to $100,000.

Rarest Books
There are countless rare books in the world, but by most experts' standards the rarest of them all is the Gutenberg Bible. It was the first book ever printed back in 1456, and although several hundred copies were originally printed finding a complete first edition would net you $25-$35 million. In today's market single pages alone go for $25K each, and several years ago just 1 volume (it's a 2 volume set) sold for $5.5M.

Rarest Necklaces
In the world of rare necklaces, a couple million dollars doesn't get you much. Even ten million dollars is cheap for these babies. The most expensive necklace may likely be one built around the Blue Empress, a rare natural blue diamond. The pear-shaped diamond weighs about 14 carats. It is set in 18k white gold and surrounded with white diamonds. It's estimated to be worth $16 million.

Rarest Wine
One of the rarest bottles of wine ever sold was purchased by Christopher Forbes for a mere £105,000 ($160,000). It was an unmarked green glass bottle with the inscription of "1787 Lafitte Th. J." (now known as Lafite and thought to be owned by Thomas Jefferson), found behind a wall in Paris.

Rarest Vases
In 2006, a 20-inch high blue and white Yuan Dynasty vase fetched over $2 million. That sounds rare but at the end of that year, casino owner Steve Wynn paid even more for a rare vase. The small copper red and white porcelain vase, is a 14th century Ming vase (pic. left) decorated in scrolling flowers. It is from the exceptionally rare Hongwu period and went for around $10.9 million, making it the world's most expensive.

Rarest Coins
As a general rule the more rare a coin is the more it's worth, so what's the rarest coin ever? It's a debatable subject as not all experts always agree, but if the Double Eagle isn't at the top of that list it's sure near it. Back in 2002 the only Double Eagle coin left to be in private hands (or so everybody thought) sold for $7.9 million dollars.

Rarest Food
Served in China for over 400 years, the primary ingredient in bird's nest soup or "Caviar of the East" is saliva nests built by cave swifts. Among one of the most expensive animal products consumed by humans it is believed to aid digestion, raise libido, and even alleviate asthma as it is dissolved in water to create a gelatinous soup. In Hong Kong, a bowl costs up to $30. Red version can cost $10K per gram.

Rarest Travel Trips
What is the rarest trip? There's no real consensus on this, but Luxist.com blogger Deidre Woodward says that the trek to summit Mount Everest still remains among the rarest trips in the world. But even this has become something that is accessible to more people. In two months and for around $60,000 you can join a group and make the attempt of a lifetime.

2008-01-05T06:49:00.000-08:00

piyushdadriwala,s creation piyushdadriwala 、秒創出

Piyush Dadriwala piyush dadriwala

Piyush, born on 10th Feb, 1967, Aquarian belongs to a middle class family in Dadri, Near Noida, elder son of Dr. Devender Kumar Goel and mother Ravikanta. piyush 、生まれて67年2月10日、水瓶座の中産階級に属していることをダドリ家族で、近くのnoida 、エルダー博士の息子と母ravikantaゴエルdevenderクマー。 I am diploma Mech Engg. 私は卒業証書engg mech 。 passed in the year 1987, creative, believe in God too much, believe in Love & Friendship, cartoonist and fond of making tarricatures, hobby of collections. は、 1987年に可決、創造は、神の存在を信じる過ぎて、愛と友情を信じて、漫画家や製造tarricatures気に入っているのは、趣味のコレクションです。

I have a unique art (mirror Image writing in two languages Hindi & English) and have written world first Mirror Image Book "Shreemad Bhagwad Gita" all 18 chapters, 700 verses in Hindi & English, besides this I have written "Shree Durga Sapt Satti" in Sanskrit Language, Sunderkand, Arti Sangrah and "Shree Sai Sach Charitra" (all 51 chapters, 308 pages, more than 1 lakh words), which kept in Sai Mandir, Sonepat for forever for devotees. 私にはユニークなアート（ミラーイメージの書き込みで、 2つの言語ヒンディー語＆英語）と世界初のミラーイメージが書かれた書籍 " shreemad bhagwad gita "全18章では、 700人の印でヒンディー語＆英語、それを除けば、私が書かれた"ドゥルガーsaptサッチshree "とはサンスクリット語、 sunderkand 、アルチsangrahと" shreeサイcharitraサッチ峠" （全51章、 308ページ、 1万ルピー以上の単語）で、サイマンディールに保管して、永遠の信者のためsonepat 。

I am very much fond of Mathematics, I have done a lot of work in Mathematics, like Points Design of Pyramid & got unique Equations, work on Pascal Triangle, A new triangle "A.P. Right Angled Triangle" in which introduced a new theorum, A very strange Table & Formula for two digits Square & Number Nine. 私は非常に気に入っているの数学、私はたくさんの仕事を完了さ数学、ポイントのようなユニークなデザインのピラミッド＆方程式は、仕事上の三角形パスカル、新トライアングル"三角形の角度のAPの権利"があり、新たに導入さtheorum 、非常に奇妙なテーブル＆フォーミュラスクエア＆ 2桁の番号ナイン。

www.piyush-g.741.com www.piyush - g.741.com

www.piyushdadriwalamaths.co.in www.piyushdadriwalamaths.co.in

pkgdwala@rediffmail.com pkgdwala@rediffmail.com

piyushdadriwala@gmail.com piyushdadriwala@gmail.com

creative piyushdadriwalaクリエイティブpiyushdadriwala

WHAT ALL GODS HAVE COMMON Edit すべての神々がどのような共通の編集

Mar 25, 2007, 5:29 pm 3月25 2007は、 5時29時まで

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9

A B C D E F G H I メッセージがある場合、私f hグラム

J K L M N O P Q R p j k信用メートルなし問研究

S T U V W X Y Z 秒トンu v W X Y Z特別

1. 1 。 HINDU ( SHREE KRISHNA) ヒンドゥー教（ shreeクリシュナ）

 1+8+9+5+5+2+9+9+1+8+5+1=63=6+3=9 1 +8 +9 +5 +5 +2 +9 +9 +1 +8 +5 +1 = 63 = 6 +3 = 9

2. 2 。 MUSLIM (MOHAMMED) イスラム教徒（モハメッド）

 4+6+8+1+4+4+5+4=36=3+6=9 4 +6 +8 +1 +4 +4 +5 +4 = 36 = 3 +6 = 9

3. 3 。 SHIK (GURU NANAK) シク（シク教ナナック）

7+3+9+3+5+1+5+1+2=36=3+6=9 7 +3 +9 +3 +5 +1 +5 +1 +2 = 36 = 3 +6 = 9

4. 4 。 PARSI (ZARA THUSTRA ) parsi （ザラthustra ）

8+1+9+1+2+8+3+1+2+9+1=45=4+5=9 8 +1 +9 +1 +2 +8 +3 +1 +2 +9 +1 = 45 = 4 +5 = 9

5.BUDH (GAUTAM) 5.budh （ gautam ）

7+1+3+2+1+4=18=1+8=9 7 +1 +3 +2 +1 +4 = 18 = 1 +8 = 9

6.JAIN (MAHAVIR) 6.jain （ジャイナ）

4+1+8+1+4+9+9=36=3+6=9 4 +1 +8 +1 +4 +9 +9 = 36 = 3 +6 = 9

7. 7 。 ESAI (ESA MESSIAH) esai （ esa救世主）

5+1+1+4+5+1+1+9+1+8=36=3+6=9 5 +1 +1 +4 +5 +1 +1 +9 +1 +8 = 36 = 3 +6 = 9

8. 8 。 SAI NATH サイナス

1+1+9+5+1+2+8=27=2+7=9 1 +1 +9 +5 +1 +2 +8 = 27 = 2 +7 = 9

AT LAST BY CAHANCE WHEN I TRY TO CALCULATE MY NAME "PIYUSHDADARIWALA" AS PER THIS METHOD ,GOT NINE......BUT I AM NOT GOD....... BUT I BELIEVE,WITHOUT GOD ,I AM DOGとうとうcahanceさを計算しようとした際に自分の名前を" piyushdadariwala "としてあたりこの方法では、 9人が....... ......しかし、私は神を信じるけど、神なしには、私は犬

9. 9 。 PIYUSHDADRIWALA piyushdadriwala

7+9+7+3+1+8+4+1+4+9+9+5+1+3+1=72=7+2=9 7 +9 +7 +3 +1 +8 +4 +1 +4 +9 +9 +5 +1 +3 +1 = 72 = 7 +2 = 9

I THINK YOU ALL ENJOY,I HAVE MORE,NEXT TIMEすべてのお楽しみだと思うよ、私はさらに、次の時間

LOVE TO ALLすべての愛を

PIYUSHDADRIWALA piyushdadriwala

www.piyush-g.741.com www.piyush - g.741.com

www.piyushdadriwalamaths.co.in www.piyushdadriwalamaths.co.in

imagination想像

amazing number nine(piyush constant) Edit 驚くほどの数の編集ナイン（ piyush定数）

Mar 25, 2007, 5:31 pm 3月25 2007は、 5時31時まで

AMAZING NUMBER NINE,(PIYUSH CONSTANT).驚くほどの数の9 、（ piyush定数です。）

IT IS VERY INTERESTING ,IT IS MY OWN SEARCH,I LOVE MATHS,IN THE FUTURE VERY SOON MY OWN BOOK ON MATHS WILL PUBLISH MATHS--- A STUDY(IN HINDI),OR MAY BE IN THE FORM OF WEBSITE.それは非常に興味深いのは、私自身を検索することは、私の愛数学、非常にすぐには、将来は、自分自身の本を出版する数学---数学を勉強する（ヒンディー語）、またはウェブサイトの形かもしれない。

TAKE ANY NUMBER OF DIGITS,HERE I AM TAKING 25 AND 32 ,NOW任意の数の数字を取る、ここで私は服用25 と32は、今すぐ

YOU CAN WRITE THEM IN FOUR WAYS LIKE THATそれらを書くことができますようにして4つの方法があります

25*32=800 25 * 32 = 800

25*23=575 25 * 23 = 575

52*23=1196 52 23 1196

52*32=1664 52 32 1664

NOW VERY AMAZING,SUBSTRACT BIGGER ONE TO ANY LOWER,ONE BY ONE今非常に驚くべきは、下部にある1つの減算大きく、 1つ1つ

1664-1196=468=4+6+8=18=1+8=9 1664年から1196年= 468 = 4 +6 +8 = 18 = 1 +8 = 9

1664-575=1089=1+0+8+9=18=1+8=9 1664から575まで= 1089 = 1 +0 +8 +9 = 18 = 1 +8 = 9

1164-800=864=8+6+4=18=1+8=9 一一六四〜八〇〇 = 864 = 8 +6 +4 = 18 = 1 +8 = 9

1196-575=621=6+2+1=9 千百九十六から五百七十五まで= 621 = 6 +2 +1 = 9

1196-800=396=3+6+9=18=1+8=9 一千百九十六から八百まで= 396 = 3 +6 +9 = 18 = 1 +8 = 9

800-575=225=2+2+5=9 八百〜五百七十五= 225 = 2 +2 +5 = 9

ALWAYS NINE,FOR ANY DIGITS,NO BODY CAN COPY ALL RIGITS RESERVED TO PIYUSHDADRIWALA,IT IS JUST MY LOVEY BLOGGERS WHO HAVE INTEREST IN MATHS.LOVE TO ALL常にナインは、任意の桁のため、体のないことをすべてコピーrigits予約piyushdadriwala 、それはちょうど私の恋ブロガーに関心を持つすべてのmaths.love

PIYUSHDADRIWALA piyushdadriwala

www.piyush-g.741.com www.piyush - g.741.com

www.piyushdadriwalamaths.co.in www.piyushdadriwalamaths.co.in

you can see all my creations私の創作のすべてを見ることができます

PIYUSH THOUGHTS piyush考え

1.TO IMAGINE IS TO HAVE EVERYTHING. 想像するには、すべての1.to 。

2.A WISE THINKS BEFORE DOING,BUT A MAD............................AFTER. 2.a賢明なことだと思って前にではなく、後にマッド............................です。

3.LOVE MAKES THE WAY TO GOD. 神への道を3.loveする。

4.PRESENT IS PAST IN FUTURE. 過去には、将来の4.present 。

5.GOD,BEFORE DYING YOU OURES,AFTER DYING WE YOURS. 5.god 、前oures死にかけている場合は、我々の後死にかけているあなたです。

6.TIME SAYS,TI-ght-ME, OTHERWISE GOING. 6.timeによれば、チタニウムght -私は、それ以外に行く。

7.PAIN IS SURE IN GAIN. 7.painは確実にゲイン。

8.WHO LOVES ALWAYS HATES. いつも愛し8.who嫌いです。

9.WITHOUT GOD A MAN JUST REVERSE OF GOD........................(DOG). 逆に、一人の男だけ9.without神犬神........................( ）。

10.A MAN OF GOD BUT A MIND OF A MAN. 10.a男の心の神ではなく、一人の男。

11.IN THIS WORLD THERE ARE LOT OF YESTERDAYS,NOT MANY TOMORROWS. 11.inこの世界にはたくさんの過去ではなく、多くの空間です。

12.LUCK,A DUCK CAN SWIM,FLY AND WALK. 12.luck 、カモはスイム 、 フライと歩いている。

13.LUCK IS AS LOCK 13.luckとしては、ロック

YOU HAVE ITS KEY あなたがその鍵

CLICK LEFT,IT CLOSES. 左クリックして、 それを閉じます。

CLICK RIGHT,IT OPENS. (READ IT CAREFULLY,AND THINK) 右クリックして、それが開きます。（注意深く読むことが、あると思われる）

14.MUCH TIME REQUIRED TO BE GOOD,TO BE BAD A LITTLE. 14.muchばよいのに要する時間は、少し不良される。

15.WE KNOW GOD,BUT GOD KNOWS US OR NOT WE DO NOT KNOW. 15.we知っている神は、 神のみぞ知るしかし、米国となかろうと知っていることはありません。

16.LOVE LAUGH AND LIVE LONG LIFE. 長い人生を生きる16.love笑う。

17.GOD IS ONE YOU ARE MANY. 1つは、多くの場合は17.god 。

18.LOVE IS "O" (+VE),DONATE IT. 18.loveは"おお" （ +ヴェ）は、寄付することです。

19.LIFE IS MIRROR,YOUR WORKS ARE IMAGES. ミラー19.lifeは、あなたの作品はイメージです。

20.LIFE IS HOUSEOF LOVE,CONFIDENCE,FAITH,SATISFACTION,DEVOTION,AMBITION,CHARACTER,HONESTY,SUCCESS AND POSITIVE ATTITUDE. 20.lifeはhouseof愛、信頼、信仰、満足感、献身、野望は、キャラクターは、正直、成功と前向きな姿勢だ。

WITH LOT OF LOVE たくさんの愛を

PIYUSHDADRIWALA piyushdadriwala

www.piyush-g.741.com www.piyush - g.741.com

pkgdwala@rediffmail.com pkgdwala@rediffmail.com

www.piyushdadriwalamaths.co.in www.piyushdadriwalamaths.co.in

email@emailaddress.com email@emailaddress.com

love愛

world first mirror image book "shreemadbhagvadgita" by piyushdadriwala 世界初のミラーイメージブック" shreemadbhagvadgita "によってpiyushdadriwala

MIRROR IMAGED BHAGVADGITA 鏡に結像さbhagvadgita

I AM PIYUSH DADRIWLA,MECH ENGG,VERY CREATIVE ,HOBBY OF COLLECTION,BELIEVE IN GOD,I WROTE GITA IN MIRROR IMAGED BY MY OWN HAND IN TWO LANGUAGES HINDI AND ENGLISH,ALL18 CHAPTERS ,700 VERSES,MEANS WILL READ IT IN FRONT OF MIRROR AND HOPE IT IS WORLD FIRST EVER HAND WRITTEN MIRROR IMAGED( ANY BOOK) "SHREEMADBHAGVADGITA".HOBBY OF COLLECTION LIKE 10,000 MATCH BOXES,300 CIGARETTE PACKETS,1045 PENS,COINS AND CURRENCIES,AUTOGRAPHS LIKE AMITABH,SACHIP,RITIQUE,LATA,ATAL,RAJIV GANDHI,INDRA GANDHI,ANIL KUMBLE,1983 WEST INDIES CRICKET TEAM,AUSTRALIAN CRICKET TEAM INDIAN WOMEN CRICKET TEAM AND OF MANY PESONALITIES,NEWSPAPER AND MAGAZINES COLLECTION,HOBBY OF MAKING CARTOONS AND CARICATURES. 私はpiyush dadriwla 、 mech engg 、非常に創造的、趣味のコレクションには、神を信じて、私は鏡に結像さgita書いた自分自身の手で2つの言語ヒンディー語と英語では、 all18支部は、 700人の印は、手段は、鏡の前で読むことと希望することは世界初の手で書かれたミラーに結像（任意冊） " shreemadbhagvadgita " 。 10000マッチ箱のような趣味のコレクションには、たばこの300パケットは、 1045ペン、コインと通貨は、サインのようなアミターブ、 sachip 、 ritique 、大腿、アタル、ラジーヴガンディーは、 インドラガンジー、アニルkumble 、 1983年に西インド諸島クリケットチームは、オーストラリアのクリケットチームの多くのインド人女性とpesonalitiesクリケットチームは、新聞や雑誌のコレクションは、趣味の製造や風刺漫画です。

WITH LOT OF LOVE たくさんの愛を

PIYUSHDADRIWALA piyushdadriwala

pkgdwala@rediffmail.com pkgdwala@rediffmail.com

www.piyush-g.741.com www.piyush - g.741.com

www.piyushdadriwalamaths.co.in www.piyushdadriwalamaths.co.in

gpalgoo@yahoo.co.in gpalgoo@yahoo.co.in

PIYUSH FORMULA AND TABLE FOR TWO DIGIT SQUARE ,IT IS NEW METHOD ,SEARCH BY PIYUSHDADRIWALA

2007-12-21T06:56:00.000-08:00

PIYUSH FORMULA AND TABLE FOR TWO DIGIT SQUARE ,IT IS NEW METHOD ,SEARCH BY PIYUSHDADRIWALA
www.piyushdadriwalamaths.co.in
www.piyushmathsworld.in

0
100
400
900
1600
2500
3600
4900
6400
8100

0
10
20
30
40
50
60
70
80
90

1
2
3
4
5
6
7
8
9
10

N2 2 = 0+(20n1 -19) n+ (2n-2) n

2

N2 2 = 100+(20n1 -19) n+ (2n-2) n

2

N2 2 = 400+(20n1 -19) n+ (2n-2) n

2

N2 2 = 900+(20n1 -19) n+ (2n-2) n

2

For Example

(1) 222 = 400 +(22 * 3 -19) 2+ (2*2-2)/2)2

= 400 +(60 -19)2 +((4-2)/2)2

=400 +(41*2)+(2/2)2

=400 +82 +2

=400+84

=484

(2) 112 = 100 +(20 * 2 -19) 1+ (2*1-2)/2)2

= 100 +40 -19 +0

=100 +21

=121

Note : n1=2 and n2=11

(3) 252 = 400 +(20 * 3 -19) 5+ ((2*5-2)/2)5

= 400 +(60 -19 )5+20

=400 +41*5+20

=420+205

=625

(4) 92 = 0 +(20 n 1 -19) n+ ((2 n-2)/2)n

= 0+(20 * 10 -19)9+ ((2* 9 -2)/2)9

=0+(200-19)9+(16/2)9

=0+(

(5) 112 = 100 +(20 * 2 -19) 1+ (2*1-2)/2)2

= 100 +40 -19 +0

=100 +21

=121

Powerful Digit “9”

2007-12-21T06:55:00.000-08:00

Powerful Digit “9”

If we research on tables, then we got some information.

(1) For the table of 2 -

By multiplication of numbers by 2 we got the following numbers which repeat themselves at some point ─

2 4 6 8 10 12 14 16 18 20 22

2 4 6 8 1 3 5 7 9 2 4

Repeat

Numbers 2 4 6 8 repeated after 9. We write it like this

2 4 6 8 1 3 5 7 9 2 4 if we add these numbers ─

2 + 4 + 6 + 8 +1 + 3 + 5 + 7 + 9 = 45 = 4 + 5 = 9

(2) For the table of 3 -

3 6 9 12 15 18 21 24 27 30

3 6 9 3 6 9 3 6 9 3

During adding we got (3 6 9) which repeat themselves.

Write it like this -

3 + 6 + 9 = 18 = 1 + 8 = 9

(3) For the table of 4 -

4 8 12 16 20 24 28 32 36 40 44

4 8 3 7 2 6 1 5 9 4 8

Repeat

4 + 8 + 3 +7 +2 + 6 + 1 + 5 + 9 = 45 = 4 + 5 = 9

(4) For the table of 5 -

5 10 15 20 25 30 35 40 45 50 55 60

5 1 6 2 7 3 8 4 9 5 1 6

Repeat

5 + 1 + 6 + 2 + 7 + 3 + 8 + 4 + 9 = 45 = 4 + 5 = 9

(5) For the table of 6 -

6 12 18 24 30 36 42 48 54 60

6 3 9 6 3 9 6 3 9 6

6 + 3 + 9 = 45 = 4 + 5 = 9

(6) For 7 table: -

7 14 21 28 35 42 49 56 63 70 77

7 5 3 1 8 6 4 2 9 7 5

7 + 5 + 3 +1 + 8 + 6 + 4 + 2 + 9 = 45 = 4 + 5 = 9

(7) For 8 table :-

8 16 24 32 40 48 56 64 72 80

8 7 6 5 4 3 2 1 9 8

8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 9 = 45 = 4 + 5 = 9

(8) For 9 table :-

9 18 24 36 45 54 63 72 81 90

9 9 9 9 9 9 9 9 9 9

9 = 9

Note :

By studying this we get knowledge about two things.

(1) In a specific table repeating of a number or some numbers.

(2) Number 9 in each equation and in the end too.

पास्कल triangle

2007-12-21T06:51:00.000-08:00

PASCAL TRIANGLE”

Pascal was not only the scientist, but also great mathematician . His efforts towards science and math were countless; Pascal triangle is a triangle upon which still some works has to done. I had also done some work on Pascal triangle; there came some points that made his invention . I studied some more on Pascal triangle then there some points came in front of me that i want to share those points with you.

Firstly we going to learn that, How this triangle is build?

If we add numbers i.e.(1+1=2) (1+2+1=4) (1+3+3+1=8) (1+4+6+4+1=16) we get (2, 4, 8, 16) ,which are even numbers.

Further reading tells, 121 is square of 11, 1331 – 11³, 14641 – (11²)², but for the solution of 11 raise to the power 5, new methods has been developed.

By using this method, we can solve any power of 11. This triangle can easily be remembered. Just remember 11, in the next number 1-1 is at the both end and just add the middle number. For example 11, 1, 2, 1, 1, (1+2), (2+1), 1 => 1, 3, 3, 1, 1, (1+3), (3+3), (3+1), 1 => 1, 4, 6, 4, 1.

Figure of Pascal Triangle

11

2
2

1
2
1

4
4

1
3

3
1

8
8

1
4

6

4
1

16
7

1
5

10

10

5
1

32
5

1
6

15

20

15

6
1

64
1

1
7

21

35

35

21

7
1

128
2

1
8

28

56

70

56

28

8
1

256
4

1
9

36

84

126

126

84

36

9
1

512
8

1
10

45

120

210

252

210

120

45

10
1

1024
7

1
11

55

165

330

462

462

330

165

55

11
1

2048
5

1
12

66

220

495

792

924

792

495

220

66

12
1
4096
1

11
11
8192
2

11²
121
16384
4

11³
1331
32768
8

11
14641
65536
7

11
161051
131072
5

11
1771561
262144
1

11
19487171
524288
2

11
214358881
1048576
4

11
2357947691
2097152
8

11
25937424601
4194304
7

11
2.85312E+11
8388608
5

11
3.13843E+12
16777216
1

33554432
2

67108864
4

134217728
8

268435456
7

536870912
5

1073741824
1

2147483648
2

4294967296
4

8589934592
8

17179869184
7

34359736368
5

115 -> 1 5 10 10 5 1 -> which is a form pascal’s triangle.

To write this in 115 from we have to use this format .

100000

50000

10000

1000

50

1

One is at sixth place .we will add five zero after it . Five is at fifth place we will add four zero .Like this we keep on decreasing number of zero…….

Add at the end we will find out sum of all values and that will be the value of (115).

161051

Is value of 115

Like this we will find out value of (1110) .

First through pascal’s triangle we get :

1 10 45 120 210 252 210 120 45 10 1 form . To

find out value we will use this format.

10000000000

10000000000

4500000000

1200000000

210000000

25200000

2100000

120000

4500

10

1

Add ten zero after 1.

Add nine zero after 10.

After 45 add 8 zero.

After 120 add 7 zero.

After 210 add 6 zero.

After 252 add 5 zero.

After 210 add 4 zero.

After 120 add 3 zero.

After 45 add 2 zero.

Add 1 zero after 10.

At the end add1.

Thisis 1110 value 25937424601

some great work done on pascal triangle,find a new way to get 11 power above 5,it took me to get this new innovation five years

“Mathematical Signs"

2007-12-21T06:32:00.000-08:00

“Mathematical Signs"

The importance of sign in our life is very clear from ancient times when words were not developed in any language in that time also people use to communicate and that was possible only with help of signs. It will not be wrong if we say that language is born from signs. Mathematics has its special place in our lives. Because people start counting…just after its birth...

This circle is not so simple to understand. But there are some means which make these things easy and those are mathematical signs. Here our main aim is to discuss the development of these signs.

These signs are use to represent work and to show relations between different mathematical numbers. In a/b the division sign (/) shows that a has to give a part to b (b divides a) and in a
In ancient hand written Granths many symbols are used but with passage of time these are same what changed and after many changes these are presented in today’s form.

Plus and Minus Signs:-

Nearly in 1960’s in the city of Bohemia there was a mathematician named Jauviderman. He wrote books on Arithmetic’s and algebra. He used the signs + and – for the first time in a book. He did not use these signs for addition and subtraction. In spite of that he used signs on behavioral bundles, to show that each bundle is more than or less than a particular fix quantity.

Sign of equality:- The sign of quality was used by Roit Recorde in 1557. He used this sign in a book of algebra ‘Behterstone of bit’ for first time. In the same book he wrote ,”I use these signs in an equation because no two things in whole world will be as equal as these two lines (=).”

Sign of Multiplication: - The sign of multiplication (X) was first time used by British mathematician Willam outred in 1631. In England people started using this sign (X) for multiplication but other countries used dot(.) as sign of multiplication

Sign of Division:- The sign of division (/) was first time used in a book of algebra written by John H. Ryan of Switzerland in 1659. This sign has prevailed in Great British and US. But other countries were using (: ) as a sign of division.

Decimal sign: - The sign of decimal was first time used by mathematician Sieman steven of Holland in his book of arithmetic’s which was published in 1585 in Leedan.In his book
; for example he wrote 173 429/1000

like this: 173. 4 (1) 2 (2) 9 (3)

this equation means that –

173 × (1/10) º + 4 × (1/10)¹ + 2 × (1/10)² + 9 × (1/10)³

Use of:-

First time use of was done by Nicole Orem (1323-1382), the mathematician of France, in his book Algorithm proportion. He wrote 7½ or 5½ like this:

½ 7 OR ½ 5

“Interesting Facts"

2007-12-21T06:22:00.000-08:00
“Interesting Facts"

Numeric system was invented by Hindus. In 5th century Aryabhatt has started the use of zero (0) but even thousand years before Aryabhatt zero known to Vedic kalkhand. Decimal Number system was given by hindus in the world.

World First university was started at Takhshila in 700 B.C. More than ten thousand students were studying around 60 subjects. Foundation of university at Nalanda was an admirable achievement of 4th century.

Mother of all European language is “Sanskrit”. According to ‘Fobars’ magazine (july 1987) Sanskit is most suitable language for compute language.

Value of PI ( ) figured by vothayan. Principle was defined by the one same whose name ‘ Pythagorean Principle’ was known for it.

Algebra , Trigonometric and calculus was given by India to the world. In 11th century Shri aacharaya gave a notation for algebric equations.

Fixed value system, Decimal number system was developed in India in 1st Century.

Who has proved the principle of Pythagoras ? Pythagoras ? No! The Principle of Pythagoras was introducing much before by ShlipSutar his birth in India history.

Who discover the Force of Gravity? Newton? No.! Famous India Astrologer Aryabhaskar charya were already introduced the force of gravity which was discovered by Newton before one thousand year approx.

Computation of the biggest star was given by mathematician chandrashekar. It is know as limit of chandrashekha by the scientists.

Ramnujan was a great mathematician who discovered the principle of probability at Cambridge university along with Pof. Hardy. He was given 100 out 100 by pof. Hardy for his fundamental brilliance whereas he himself got 25 In that way Prof Hardy has great respect for Ramanujan in his heart.

Zero (0) was finalized and decimal system was discovered in India by Hindu Gurus.

According to classical Hindu mathematician also known as Vedic Mathematics to make it possible for oral answer of complex mathematician question defined in due or two lines.

For calculation of sangria ganak in Binary number was provided by Hindu Prans thousand years before its existence. In binary number system. The digit can be either 0 (negative) or 1(positive) . All the digit are combinations of 0 and 1 . Our ancient philophical teaties says “The whole world is made up of means positive and zero means negative”.

They said that:-

Elbert Einstein:- we are grateful to India who taught us counting, without which nothing is possible for scientific research.

Prof BryaN David Josephso(France):- youngest novel winner Hear and ideal system in vedant and numeral which is like a quantum field that is Atomic and partial level of particles for process and distribution is its key.

merajnansabkaapna

2007-12-15T07:17:00.001-08:00

merajnansabkaapna

2007-12-13T05:58:00.001-08:00

spock

2007-12-12T06:11:00.000-08:00

Flickr

2007-12-07T07:25:00.001-08:00
This is a test post from , a fancy photo sharing thing.

collection6

2007-12-07T06:34:00.001-08:00

COLLECTION7

2007-12-07T06:33:00.001-08:00

COLLECTION 9

2007-12-07T06:31:00.001-08:00

COLLEC TION10

2007-12-07T06:29:00.001-08:00

collection 11

2007-12-07T06:28:00.001-08:00

collection 12

2007-12-07T06:26:00.003-08:00

collection 12

2007-12-07T06:26:00.001-08:00

my world famous work on mirror image books

2007-12-07T06:23:00.001-08:00

how to write words in mirror image

2007-12-07T06:22:00.001-08:00

vastu

2007-09-17T06:36:00.000-07:00
VASTU AND DIRECTIONS
As per the Vastu rules, while constructing a building it must be located in such a way that it receives the maximum benefit from the solar and cosmic energies. Thus the orientation attains a vital part. The various directions are:

North, South, East, West, NorthEast, NorthWest, SouthEast and SouthWest. Every corner is again divided into 2 sides. Namely:

NorthEast - East North EastNorth North East
SouthEast - East South East South South East
NorthWest - West North WestNorth North West
SouthWest - South South West West South West

The NorthEast corner is stated to receive the cosmic energy, which is a combination of energy from different planets apart from sun, in abundance. And from there it moves in the opposite direction i.e to the SouthWest.

Vastu Tips Pyramids
Vastu Principles Vastu Test
Vastu Consultancy Pyramid Chips
VASTU TIPS

Astroshastra adapts the ancient vastu guidelines for the contemporary Western lifestyle by offering a reliable system to help you determine your specific needs and preferences.

Vastu can be integrated as science based on energy emanating from various sources. Energy pervades nature. Our life depends on it. Energy rules every form of life on earth. This energy can be either positive or negative. Incorrect vastu creates negative energy. Vastu corrections can be done by neutralising this negative energy by strong positive energy radiating devices like energised pyramids and Energy cards.

Astroshastra shows you practically and concretely how to align the elements of space, air, fire, water and earth so that they work best for you. You will discover the right place to put your bed in your bedroom, the right direction for you to face when you work, the right location to take a healthy break, the right place for your children to study, the right location for your computer or TV, the right place to put heavy furniture, the right place for pictures of your loved ones.

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TIPS FOR YOUR HOME

Vastu can fruitfully be applied to the areas of our activities. We should initially concentrate on areas, which affect our life, i.e., where we live and work.

We all care about our homes and spend time, effort and money, trying to make them more comfortable. For most of us it represents one of the biggest investments we ever make. Our home (the architecture of our homes) can damage our health, the air we breathe and the water we drink, without our even being aware of it.

Similarly, at the places where we work, environmental stresses contribute to overall load, preventing us to reach our full potential. Resisting these external forces becomes more important for growth and development.

Your Prayer Room

1 Room for prayer and meditation is recommended to be in the north-east corner of the house.
2 Deity or image of god should not face the south direction. Ideal positions are such that you face east or west while praying.

Your Staircase

1 Southern or south-western portions of the building are ideal for locating staircase.
2 Do not design staircase of a building in the north-east portion.
3 The steps should climb from east to west or from north to south.
4 If there are landings or turnings in a staircase, it should wind up in the clockwise direction.
5 The number of steps in a staircase should be an odd number so that if you start climbing the steps with the right foot, you will reach the higher floor on the right foot itself.
Number of columns in a building
Columns in a building should be in even numbers.
Columns in the north-east corner should not be circular.
When columns are exposed for architectural purposes, the number of exposed columns also should be even.

VASTU TIPS (Contd..)
Bedroom:- While construction a bed - room, directions should be specially chosen. The directions according to which rooms should be constructed are as under:

North-West The room in this direction is suitable for guests and girls.

South-West The Chief of the house should have his room in this direction.

North-East No bedroom should be situated in this direction. In such situation there is a possibility of increase number of girls in the family

South-East No bedroom should be located in this direction. The children do not take interest in studies. There is no sound sleep. People have much anger. Decisions are generally taken hurriedly.

West There is a possibility of birth of larger number of girls in the family.

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Bathroom: - It should be in the West and South directions and the flow of its drains should be towards North-East. Commode should be South or West facing. Exhausts fan can be fixed on North and East walls. Geysers should be South-East since it is 'Agneya' corner and Geyser is associated with heat.

Toilet: -According to Vastu principles, Toilets and Bathroom should be situated separately. These days, it is not possible because of paucity of space. As such, these are built attached with each other within the house. The following points need special attention for such construction.

1. Never build toilets in the direction of eastern corner or at "Ishan angle".
2. These should be constructed mainly towards South or West.
3. The face should be towards soutrh or West while discharging stool.

Balcony: - It should be constructed in the North-East to achieve good health and wealth and if in the houses already constructed, the balcony is in South-West, it should be covered with glass or screens.

Cowshed: - It has been scientifically proved that the cow discharges Methane gas. We exhale carbon dioxide, which is harmful. Methane nullifies the pollution of Carbon dioxide. Therefore cows should be kept in the North-West as far as possible.

Children's Room: - The children are future of the nation. If the parents are able to give right direction to the children at their tender age then tomorrow they will turn into disciplined citizens. The children's room, too, should be constructed in the North-West corner but the bathroom should be arranged in above noted direction only.

Doors: - The doors should be in the North and East. When someone enters through the door, the waves emerging from the doors affect his mind because the magnetic waves always flow around us. Some painting or window should be opposite each door.

Drawing Room: - It should be in North-West, South or west direction. In the traditional drawing rooms mattresses, covered with white sheets of cloth are spread in the entire room and round pillows are kept in South and West walls. Similarly, in the modern drawing room, the furniture should be kept in South and West directions. As far as possible the open space should be maximum in North and East directions.

Dining Room: - In olden days the meals were taken in the kitchen itself but now the dining room has become an integral part of the drawing room. However the dining table should be kept in South-East.

Delivery Room: - If the delivery of child is to be made in the house, it should be done in North-West rooms.

Entertainment Room: - This is an important place and the suitable directions for it is North-West or South.

Food Storage: - The store should be in the kitchen and in the South-East corner.

Garages: - It should be in the South-East or North-West corner but load on North and East Walls be kept at the minimum.

General Room: -Though, it is sparingly used; yet it should be constructed in the North-West.

Guest Room: - It should be in North-West corner.
VASTU TIPS (Contd..)

Kitchen: -The kitchen must be situated in fire angle, i.e. in South-East. The face of the cook should be towards the East. The water tap in kitchen should be in the North-East direction. It is better if the stone on which food is cooked, is of red colour.

North-West This direction is the source of air. Fire and air are combined. As such, the kitchen can also be built in this direction. But while cooking, the face should be towards the East only.

South-West This direction is not suitable for kitchen.

North-East This direction represents the place of water. Fire and water are not friends. Hence, the kitchen should not be located in this direction. If there is a tank or well in this direction, it is all right or otherwise, as has been experienced, it would curtail peace and mutual love in the family.

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Laundry: - As the hot water is also used while laundering the clothes, the South-East corner has been considered best for it but the flow of drains should be towards North-East.

Main Switch: - The junction of electric cables of the house should be in the South-East corner along with the main switch.

Main Gate: - The main gate is dependent upon the direction on which the plot lies. However, Both-East and West directions are considered best for the main gate of the house.

Mezzanine Floor: - According to the rules of Vastu-Shastra we have to keep the South-West portion higher. Therefore the mezzanine floor should be constructed in, South or West.

Open Space: - In every plot more open space should be kept in North, East and North-East than in South and West.

Portico: - It should be in the Borth-East and its height should be less than that of the main roof.

Patient's Rooms: - It is best to keep this room in South-West or North-West corner. If the head of the patient is kept in the South, he recovers early.

Place of Worship: - This is the place from where good ideas flow. If it is in the North-East and the face of the idol is towards North or East then the property of the house is assured. To gain knowledge, one should offer worship keeping his face Northward and should sit near the northern wall and to gain economic prosperity one should keep one's face towards East and should sit in the Eastern side of the room.

Servant Quarters: - These should be in the North-West corner. But load on the north and east walls should be kept at a minimum. This will keep the servants also happy.

Stair Case: - According to the principles of Vastu Shastra the staircase can be constructed in any direction except North-East. If in some old house, the staircase is in the North-East, then a room should be constructed in South-East to lessen its ill-effects.

Study Room: - The North-East corner is best for a study room. If the study room and place of worship room are adjacent then it is considered most beneficial.

Safe(Cash): - Petty cash for daily expenses should be kept in the North. Jewelry and other valuables should be kept inside a safe in the South. This adds to prosperity.

Terrace: - It should be in the North-East.

Trees: - These should not be in North and East but in South and West only.

Verandah: - This should be in the East as this is also a form of open space. Water Tank/Overhead

Water-Tank: - It is best to keep it in the North-West, but could be kept in West also

VASTU TIPS - Contd..

Well & Tube well: - Water, too, enjoys great importance in Vastu-Shastra, so it should be in the Eishan Kona or North-East corner which is the most suited direction for it. It has been observed that if a well or tube well was in any other direction, the house owner suffers heavy losses. But when it was closed and the tube well was constructed in the North-East, the owner started earning profits. Given below are the directions and their effects.

North Peace and Happiness

East Extreme wealth

South Shortage of female members or miseries.

West Stomach and sexual troubles among male members.

North West Enemy creates trouble.

South - West Disagreement with the son.

South-West Fear of death.

Center of the House Causes Heavy monetary losses

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Windows: -These should be opposite to the doors so that both the positive and negative cycles could be completed. This provides happiness and progress to the family.

Watch & Ward: - The guard- room is always constructed by the main gate. Its height should never be more than seven feet.

Weights & Equipment: - For these the South-West direction is considered to be the best.

Yoga & Meditation: - These should always be done in the open and in the North-East direction.

TIPS FOR FACTOR

1. For factory we should select 'SHERDAH' plot. This type of plot has been considered very beneficial.
2. The shape of the land, roads, uninterrupted availability of water and electric power etc. should be kept in mind.
3. According to 'Vastu Shastra' the main gate of factory should be kept in the East, North or North-East of the plot. All other doors can be kept in North-East, East, North or North-West.
4. The guardroom of the factory should be in North-West of the Northern gate and to the South-East of Eastern gate.
5. There must be open space in the North- East. The land of the factory should be elevated in South-West.
6. The store of the factory should be in the South-West.
7. The North-West corner should be used for car-parking.
8. The administrative block should either be in the North or in the East.
9. The South-East and North-West corner should be selected for the staff.
10. For lavatory and toilet the North-West or South-East corner are most suitable.
11. For heavy machinery South, West or South-West corner is best and these directions are also suitable for raw materials.
12. Semi-finished goods should be kept in the West. With this scheme, the finished product will have uninterrupted sale.
13. Transformers, boilers, oil engines, generators etc. should be kept in South-East corner.
14. The North-East portion of the factory should be lower than the South-West portion.
15. The production process should commence in the South-West and the final product should emerge from North-East.
VASTU TIPS - FOR OFFICE

Vastu is like a mechanism. It is directly related to your destiny. So it will always help to improve it. For example if you have a car you cannot expect it to give you the performance of an air craft. Likewise a good Vastu will always improve your financial status and working conditions.

1 Money and valuables should be kept in an Almirah or safe facing north.
2 If north is blocked it can be cured with the help of regulators.
3 If north of any house is blocked it blocks prosperity.
4 A boring or tube well in south is very harmful for finance.
5 A pit or under ground tank in south is also very harmful for finance. Certain pictures of god goddess and proper placement of mirrors brings financial gains in the house.
6 Water flowing from north to east is very good.
7 A water fountain in the north east part of the house or factory is very good.
8 An aquarium with 9 gold fish and one black fish, in the north east corner/portion of the house or factory is very good.

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SOME IMPORTANT RENOVATIONS WITHOUT DEMOLITION:

I have often seen that at many places, that construction has been done against the principles of Vastu and no improvement is possible without demolition. At such places, I have made some experiments, which have proved to be successful. These are stated below:-
1) If some river or drain is flowing in a direction other than the north-east direction of the house and has anti - clock movement, then I advised to place the statue of dancing Ganeshji facing the west o n the north-east corner of the house. It yielded good results immediately.
2) If the boring has been done in the wrong direction in a house or a factory, then I advised to place the picture of Panchmukhi Hanumanji, facing South-East to the boring. I have seen that bad effects due to wrong boring have subdued.
3) If a naked wall is seen while entering into a flat, then either a picture or a statue of Ganeshji should be placed there. The naked wall is the sign of loneliness. Hence, the wall should not be kept naked.
4) If high voltage overhead wires pass over a house, then a plastic pipe filled with lime should be erected from one corner to the other of the affected area in such a manner that its both ends should remain outside by at least three feet each. This will eliminate the evil effects of energy being generated out of the overhead wire.
5) In certain cases, energy circles can be improved by using Swastika Yantra. But, this requires a lot of care. This should be handled under the supervision of an able Vastu Consultant.

WHAT IF? EFFECT
SOLUTION
kitchen is at the North -East direction. It would curtail peace and mutual love in the family. The kitchen can be built in North - West direction. But while cooking, the face should remain towards the east only.
kitchen is at the South-West direction. This direction is not suitable for kitchen. It would be harmful for the land lord. South-East direction is best for the kitchen. Water tap in the kitchen should be in the North-East direction. It is better if the stone, on which food is cooked, is red.
Tube well is not at the suitable direction. Shortage of female members, sexual and stomach troubles among male members. North -East direction is best for Tube well or well. This place should be open and at the lowest level of the house.
Toilet is built at the eastern corner at the 'Ishan' angle. It may be cause of diseases. This should be constructed mainly towards South or West. The face should be towards north or West while discharging stool.
Bedroom is at the South -East direction The children do not take interest in studies. There is no sound sleep. People have much anger. Decisions are generally taken hurriedly. To know about best direction for the bedroom, click here.
Bedroom is built in the North - West direction. The room in this direction is suitable for guests and girls.
Worship place is not at right direction Loss of concentration. Unpeaceful mind To see the good direction of worship place, click here

VASTU TIPS (Contd..)

REMEDIES FOR CONSTRUCTION MADE AGAINST THE PRINCPLES OF VASTU

Bedroom:- While construction a bed - room, directions should be specially chosen. The directions according to which rooms should be constructed are as under
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1 If some river or drain is flowing in a direction other than the north-east direction of the house and has anti - clock movement, then it is advised to place a statue of dancing Ganeshji facing the west on the north-east corner of the house.
2 If the boring has taken place in the wrong direction in a house or a factory, then it is advised to place a picture of Panchmukhi Hanumanji, facing South-West to the boring.
3 If high voltage overhead wires pass over a house, then a plastic pipe filled with lime should be erected from one corner to the other of the affected area in such a manner that its both ends should remain outside by at least three feet each. This will eliminate the evil effects of energy being generated out of the overhead wire.
4 In certain cases, energy circles can be improved by using Swastika Yantra. But, this requires a lot of care. This should be handled under the supervision of an able Vastu mason.
5 While drinking water keep your face towards North-East.
IMPORTANT TIPS

1 Cactus should not be planted or kept in the house.
2 The statue of Hanumanji should not be placed in South-East. It may create fire hazard.
3 All the doors should open inside so that the energy may remain inside.
4 The hinges of doors should be noiseless. If so. The hinges may be greased periodically.
5 The doors should open towards right hand.
6 Bed should not be put under a beam.
7 There should not be five corners in the ceiling of a room.
8 Efforts should be made a leave the rooms open on North-East side.
9 While ascending the staircase, the face should be either towards the north or the east.
10 The seat of the toilet should face North-South.
11 No doors or windows should be provided on South-West side.
12 Almirahs and beds should be set very close to the South - West wall and at a distance from the north - east wall.
13 When sitting for worship, keep your face towards North-West and sit in that corner to intake air from that direction.
14 While Taking meals the plate should be in South-East.
15 In the South-West Corner of the house one should sleep pointing his head towards south.

NUMBER NINE ,AMAZING

2007-09-15T07:35:00.000-07:00
NUMBER NINE ,AMAZING

* NINE GODDESS
**NINE PLANETS
***PIYUSH CONSTANT
AMAZING NUMBER NINE,(PIYUSH CONSTANT).
IT IS VERY INTERESTING ,IT IS MY OWN SEARCH,I LOVE MATHS,IN THE FUTURE VERY SOON MY OWN BOOK ON MATHS WILL PUBLISH MATHS--- A STUDY(IN HINDI),OR MAY BE IN THE FORM OF WEBSITE.
TAKE ANY NUMBER OF DIGITS,HERE I AM TAKING 25 AND 32,NOW
YOU CAN WRITE THEM IN FOUR WAYS LIKE THAT
25*32=800
25*23=575
52*23=1196
52*32=1664
NOW VERY AMAZING,SUBSTRACT BIGGER ONE TO ANY LOWER,ONE BY ONE
1664-1196=468=4+6+8=18=1+8=9
1664-575=1089=1+0+8+9=18=1+8=9
1164-800=864=8+6+4=18=1+8=9
1196-575=621=6+2+1=9
1196-800=396=3+6+9=18=1+8=9
800-575=225=2+2+5=9
ALWAYS NINE,FOR ANY DIGITS,NO BODY CAN COPY ALL RIGITS RESERVED TO PIYUSHDADRIWALA,IT IS JUST MY LOVEY BLOGGERS WHO HAVE INTEREST IN MATHS.LOVE TO ALL
PIYUSHDADRIWALA
www.piyush-g.741.com
www.piyushdadriwalamaths.co.in

*ALBET EINSTEN,S EQUATION
E=MC(SQUARE)
E=ENERGY,M=MASS AND C=SPEED OF LIGHT(THAT IS3*10 POWER 8)
THAT IS 9*10POWER16,THAT IS FACT ,IF YOU MULTIPLE NINE TO ANY NUMBER OF DIGITS ,THE SUM OF EACH DIGITS YOU WILL ALWAYS GET NINE.
*WHAT ALL GODS HAVE COMMON ,THAT IS ALSO NINE.

1 2 3 4 5 6 7 8 9
A B C D E F G H I
J K L M N O P Q R
S T U V W X Y Z

1. HINDU ( SHREE KRISHNA)
1+8+9+5+5+2+9+9+1+8+5+1=63=6+3=9
2. MUSLIM (MOHAMMED)
4+6+8+1+4+4+5+4=36=3+6=9
3. SHIK (GURU NANAK)
7+3+9+3+5+1+5+1+2=36=3+6=9
4. PARSI (ZARA THUSTRA )
8+1+9+1+2+8+3+1+2+9+1=45=4+5=9
5.BUDH (GAUTAM)
7+1+3+2+1+4=18=1+8=9
6.JAIN (MAHAVIR)
4+1+8+1+4+9+9=36=3+6=9
7. ESAI (ESA MESSIAH)
5+1+1+4+5+1+1+9+1+8=36=3+6=9
8. SAI NATH
1+1+9+5+1+2+8=27=2+7=9
AT LAST BY CAHANCE WHEN I TRY TO CALCULATE MY NAME "PIYUSHDADARIWALA" AS PER THIS METHOD ,GOT NINE......BUT I AM NOT GOD.......BUTI BELIEVE,WITHOUT GOD ,I AM DOG
9. PIYUSHDADRIWALA
7+9+7+3+1+8+4+1+4+9+9+5+1+3+1=72=7+2=9

I THINK YOU ALL ENJOY,I HAVE MORE,NEXT TIME
LOVE TO ALL
PIYUSHDADRIWALA
www.piyush-g.741.com

www.piyushdadriwalamaths.co.in

PIYUSH MIRROR IMAGE WORDS(CAPITAL )

2007-09-15T07:11:00.000-07:00
PIYUSH MIRROR IMAGE WORDS(CAPITAL)
THIS IS MY OWN CREATION ,ONE DAY I WAS DOING WORKING ON MIRROR IMAGE WRITTING,SUDDENLY ONE IDEA CAME IN MY MIND AND I GOT SOME ALPHABETS,WHICH NEVER CHANGE IN MIRROR ,THIS ALPHABETS ARE (A,H,I,M,O,T,U,V,W,X,Y),AND AFTER THAT I WORKED ON WORDS ,WHICH I GOT,FIRST I GOT A WORD WHERE I WAS WORKING THAT IS "YAMAHA",THEN "OHIO,TOYOTA,(THERE ARE ALL JAPANES WORDS MAY BE MORE IN THIS LANGUAGES,THEN I GOT
AIM
AM
AMITY
AT
AMOMUM
ATOM
ATAXIA
ATOMY
AUTO
AUTOMAT
AWAIT
AXIOM
AWAY
IT
TOO
TO
OX
MIX
WAX
MAXIM
WITH
HIM
THAT
WHAT
WHY
HOW
MAY BE MORE ,IF YOU HAVE MORE ADD.....
PIYUSHDADRIWALA
www.piyushdadriwalamaths.co.in
www.piyush-g.741.com
www.piyushdadriwala.4t.com
www.piyushdadriwala.3steps.com

प्य्रामिद ऎंड sphere

2007-08-27T07:17:00.000-07:00
Pyramid and Spheres
Pyramids are polyhedra because they are made up of plane faces. Spheres are not polyhedra because they are curved.

Pyramids
If a line that is fixed at a point, called the vertex, is moved around the perimeter of a polygon, then a pyramid is formed.

The following solid is pyramid.

Pyramids are named after their base. So, the pyramid shown above is an example of a rectangular pyramid.

Some other pyramids are shown below.

A pyramid is said to be right when its vertex is directly above the centre of the base. The cross-sections parallel to the base are the same shape but have different sizes.

The net of the above pyramid consists of:

a rectangular base; and
four triangular faces

Note:
The cross-sections parallel to the base have the same shape as the base but different sizes.
The net of a pyramid consists of a base polygon and a number of triangular faces.
A regular pyramid has a base that is a regular polygon and has faces which are isosceles triangles.

Spheres
If a semicircle is revolved about its diameter, then a sphere is formed.

The following solid is a sphere.

The cross-sections of a sphere are circles. The cross-sections that pass through the centre of the sphere are called great circles whilst other cross-sections are called small circles.

A hemisphere is a half sphere.

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pyramid

2007-08-27T06:46:00.000-07:00
The curious synchronicities of the pyramids

The use of the cross and plumb line reveal several mathematical designs that co ordinate with time speed and distance of the motions of the earth, sun and moon against the zodiac thereby implying that the designer of the complex understood astronomical mathematics not considered to have appeared historically until several thousand years later.

Click on thumbnails

The Giza Complex near Cairo in Egypt offers many mysteries to solve and is laid out in a complex of 3 larger pyramids and six small ones amounting to a total of 9

Essentially, the complex is located at 30° north Latitude

Did the architect astronomer design the pyramids to reflect their own latitude?

In essence the reducing circumference of a small circle as you progress from the south equator to the north pole south to north is 240 nautical miles per degree

A degree is equal to 60 nautical miles at the equator and 1 nautical mile = 1 arc minute of time/speed/ distance

Speed of the sun over a great circle is 900 nautical miles per hour and is directly related to the speed of earth rotation

360° x 60 minutes = 21600 Nautical miles earth circumference at the equator this number is directly related to 2160 years in an astrological age because of the symbiotic geometry

The pyramid is at 30 degrees North

30 x 240 = 7200 - 21600 = 14400 nautical miles earth circumference at 30 degrees latitude

Each face of the pyramid is 180 degrees

180 x 4 = 720 take the seen and the unseen as in the squaring of the circle exercise

720 x 2 = 1440 x 10 equals 30 latitude at Giza of a small circle circumference of 14,440 Nautical miles.

Did the architect astronomer show in the pyramids a knowledge of Precession?

Motion of the Precession of the Equinoxes

Multiply by three main pyramids 720 X 3 = 2160 an astrological age

9 pyramids in the complex X 720 x 4 = 25920 years or 12 Zodiac signs

Did the Astronomer Architect measure the motion of the moon?

25920 - 21600 = 4320 x 4 = 17280 years

The moon is retrograde and only travels at 720 miles per hour and is related to the base line of one side of the great pyramid as 720 feet

in 24 hours it travels 17280 miles on a great circle

1 hour for the sun in distance of rotation 900 Sea Miles

1 hour for the moon in distance 720 sea miles

900 - 720 = 180° = or 1 face of the pyramid in degrees

52° x 52° x 76 °= 180° squares the circle and incorporates the Golden Section and perfect spherical geometry relating to

As Above so below.

Did the Astronomer Architect need an instrument capable of measuring degrees as a sidereal observation?

Measuring the path of a celestial object with a cross and plumb line

Are the Dixon Relics the missing Architects Instrument?

Dixon relics assembled

Was the Pyramid a clock?

On the matter of time
The earth spins at 900 nautical miles every hour (Unit of Horus) or 60 minutes of arc

60 ÷ 900 = 0.0666 minutes of time
1 minute of arc at any latitude = 0.0666 minutes of time

24 hours x 60 minutes = 1440 minutes

24 hours x 60 minutes x 60 seconds = 86,400 seconds ÷ 4 = 21600

1440 ÷ 21600 = 0.0666

Earth measurement is the secret of time and that is governed by cycles of life, death and rebirth
These cycles were measured by observing the constellation Draconis in the North as it spins known as Shiva, The Serpent, The Lord of the Dance, the worm, the dragon, the millstone and Reret.
There is much more of course, but it was the 1872 Dixon Relics that allowed Crichton E M Miller to re construct the astronomer, navigator architects instrument to rediscover this curiosity of number and synchronicity in the Giza Complex

piyushdadriwala
www.piyushdadriwalamaths.co.in

pyramids

2007-08-27T06:27:00.000-07:00
Geometry > Solid Geometry > Polyhedra > Pyramids
Recreational Mathematics > Interactive Entries > LiveGraphics3D Applets

Pyramid

A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex (known as the "apex"). A right pyramid is a pyramid for which the line joining the centroid of the base and the apex is perpendicular to the base. A regular pyramid is a right pyramid whose base is a regular polygon. An -gonal regular pyramid (denoted ) having equilateral triangles as sides is possible only for , 4, 5. These correspond to the tetrahedron, square pyramid, and pentagonal pyramid, respectively.

A pyramid is self-dual, corresponding to the fact that a pyramid's skeleton (a wheel graph) is a self-dual graph.

An arbitrary pyramid has a single cross-sectional shape whose lengths scale linearly with height. Therefore, the area of a cross section scales quadratically with height, decreasing from at the base () to 0 at the apex (assumed to lie at a height ). The area at a height above the base is therefore given by

(1)

As a result, the volume of a pyramid, regardless of base shape or position of the apex relative to the base, is given by

(2)
(3)
(4)

Note that this formula also holds for the cone, elliptic cone, etc.

The volume of a pyramid whose base is a regular -sided polygon with side is therefore

(5)

Expressing in terms of the circumradius of the base gives

(6)

(Lo Bello 1988, Gearhart and Schulz 1990).

The geometric centroid is the same as for the cone, given by

(7)

The lateral surface area of a pyramid is

(8)

where is the slant height and is the base perimeter.

Joining two pyramids together at their bases gives a dipyramid, also called a bipyramid.

piyushdadriwala
www.piyushdadriwalamaths.co.in

Indira Gandhi

2007-08-14T01:51:00.000-07:00
Indira Gandhi
Indira Gandhi was the first woman ever elected to lead a democracy. She was the Prime Minister from 1966-77 and then again between 1980-84 till her death at the hands of her own bodyguards. A paradox she may seem for during the time that she served India as a Prime Minister, she was known as a dictator as well as one of the most charismatic leaders of India.

Indira Gandhi was born on November 19, 1917 and was the only child of Jawaharlal and Kamala Nehru. The active participation of both her parents in India's independence struggle of India from the British, Indira Gandhi was drawn to politics at an early age. It was as if politics and politicians always surrounded her.

By the time she was about twelve years old, she headed what came to be known as the Monkey Brigade. The monkey brigade consisted of children who warned the independence movement leaders of their arrest. Being its leader, she delivered speeches while other children actually warned the people who were going to be arrested. The Congress figured that the British would not suspect children of participating in such involvement.

She was soon sent to England for her studies where she joined the Somerville college, Oxford. She also spent time in Switzerland primarily because her mother needed to be there due to her ill health. But her mother passed away in 1936.

In 1938, Indira returned to India and joined the Indian National Congress Party. Soon afterwards in 1942, she married journalist Feroze Gandhi with whom she eventually had two sons-Sanjay and Rajiv Gandhi. Soon after the couple was married, they were sent to prison on charges of subversion by the British. Her one and only imprisonment lasted from September 11, 1942 until May 13, 1943 at the Naini Central Jail in Allahabad.

India won its independence from Britain in 1947. In that same year, Indira's father Jawaharlal Nehru became India's first Prime Minister. Since her mother's death, Indira acted as her father's hostess and confidante and traveled with Nehru. Simultaneously, she was steadily making her way presence felt in the political arena. She began to associate herself with numerous organizations. From 1953-57 she was Chairman of the Central Social Welfare Board. In 1955, she became a member of the Working Committee and Central Election Committee, the Central Parliamentary Board from 1956, and was the President of the All India Youth Congress from 1956 to 1960.

After the death of her father, Jawaharlal Nehru in1964, the then Prime Minister Lal Bahadur Shastri appointed Indira Gandhi as the Minister of Information and Broadcasting. This position was the fourth highest-ranking position in the Cabinet as radio and television were an important source to disseminate information to the largely illiterate population of India. As a minister, She encouraged the making of inexpensive radios and started a family planning program.

But Lal Bahadur Shastri suddenly died of a heart attack in 1966. The contenders for Prime Minister's post could not agree among themselves and therefore felt that Indira Gandhi would be the best for the position as a prime minister. Hence, she became the Prime Minister in 1966 till India held the next elections in 1967. She won that election--- in 1967, she became the first woman ever elected to lead a democracy. In 1971, Gandhi was re-elected by campaigning with the slogan "Garibi Hatao" (Abolish Poverty).

She rode a wave of success in 1971 with India's victory in the Indo-pak war and the launching of the India's first satellite into space. And with the testing of a nuclear device in 1974, she earned the reputation of a tough and shrewd politician among the middle class.

Simultaneously, by 1973, large-scale demonstrations were taking place across Delhi and north India. A large section of the population felt that she was not living up to her promises of "Garibi Hatao". High inflation, rampant corruption and poor standards of living were leading to social unrest.

In an attempt to control population growth, she implemented a voluntary sterilization program. But her adversaries criticized it. She began to face a strong opposition to her administration in general.

By 1975, Indira Gandhi had to face charges of corruption. In June 1975, the High Court of Allahabad found her guilty of using illegal practices during the last election campaign. She was ordered to vacate her seat. There were demands for her resignation.

She responded by declaring a state of emergency on June 25, 1975. During this emergency, the Supreme Court of India overturned the Allahabad High Court's judgment. Through the powers ensured to her through the emergency, she ordered the arrests of the main opposition leaders. In her opinion, she declared an emergency for the good of India. The constitutional rights of the citizens were limited and the press was under strict censorship overnight. Meanwhile, her eldest son, Sanjay Gandhi, ordered the removal of slum dwellings, and in an attempt to curb India's growing population, initiated a highly resented program of forced sterilization.

In early 1977, she thought she had eliminated her opposition and called for fresh elections. Her Congress party lost badly at the polls. She was voted out of power and a newly formed coalition of political parties came to power. Many declared that she was a spent force. But, three years later, she was to return as Prime Minister of India.

Indira Gandhi came to power again as the prime minister in 1980. The same year, however, her son Sanjay was killed in an airplane crash.

In the post-emergency period, as a prime minister Indira Gandhi was preoccupied by efforts to resolve the political problems in the state of Punjab. In her attempt to crush the secessionist movement of Sikh militants, led by Jarnail Singh Bindranwale, she ordered an assault upon the holiest Sikh shrine in Amritsar, the "Golden Temple". It was from here that Bindranwale and his armed supporters waged their campaign. "Operation Bluestar", waged in June 1984, led to the death of Bindranwale, and the Golden Temple was stripped clean of Sikh terrorists. However, the Golden Temple was damaged, and Mrs. Gandhi earned the undying hatred of Sikhs who bitterly resented her action in their sacred space. In November of the same year, Mrs. Gandhi was assassinated, at her residence, by two of her own Sikh bodyguards, who claimed to be avenging the insult heaped upon the Sikh nation.

Her death led to sectarian violence across India during which over a 1000 people died of which many were Sikhs.

Indira Gandhi was remarkable for her ambition for personal power, her endurance and political tenacity. Mrs. Gandhi acquired a formidable international reputation as a "statesman", and there is no doubt that she was extraordinarily skilled in politics. On the international front, she insisted on India's independence, gradually loosened ties with the former USSR that were developed in the early 1970s when China seemed menacing. She was proved to be a forceful spokeswoman for the rights of poorer nations. On the domestic front, however, her autocratic methods often clashed with her democratic principles. She had an authoritarian streak and rarely tolerated dissent. In many respects, Indian democracy was irreparably harmed during her rule. Apart from her infamous imposition of the internal emergency, the use of the army to resolve internal disputes greatly increased in her time.

After her death, her second son, Rajiv Gandhi, was sworn in as head of the Congress party and Prime Minister.

Quick Look : : Life Line
1917, November 19: Date of birth
1930: founded the Bal Chakha Sangh and was part of the Vanas Sena---a children's organization which ran messages to help the Congress Party or Freedom Movement during the non-cooperative movement.
-Goes to study in England and joins Somerville college in Oxford.
1938: joins the Indian National Congress
1942: marries Feroze Gandhi
1942: The couple is soon imprisoned at the Naini Central jail, Allahabad on September 11, 1942 on charges of subversion
1943, May 13: released from Naini Central jail
1947-1964: remains with her father as his hostess and close supporter
1947: under Gandhi's instructions, she works in riot-affected areas of Delhi.
1953-57: serves as the Chairman of the Central Social Welfare Board
1955: becomes a member of the working Committee and Central Election Committee
1956: member of Central Parliamentary Board
1956-60: Becomes the President of the All India Youth congress
1960: Feroze Gandhi, her husband, dies
1964: Nehru, her father, dies
1964: she is elected to the parliament in his place
1964-66: serves as the Minister of Information and Broadcasting
1966: becomes the Prime Minister after the death of Lal Bahadur Shastri
1971: calls for a general election and wins by an enormous margin
-declares war with Pakistan over Bangladesh
-sends India's first satellite into space
-her period in office is marked by severe economic troubles.
1973: there are demonstrations across the country due to high inflation, poor state of the economy, rampant corruption and the poor standards of living.
1974: tests the explosion of a nuclear device.
1975, June: the High Court of Allahabad found her guilty of illegal practices during the last election campaign and ordered her to vacate her seat.
-She responded by declaring a state of emergency.
1977: Indira Gandhi calls for early elections but loses
-she faces charges of corruption and authoritarianism
-is expelled from parliament and is imprisoned.
1978: is released from prison.
-Resigns from the congress party
-Becomes leader of the Indian National Congress
-Wins a seat through a by-election
1980: is re-elected as the Prime Minister
-Sanjay Gandhi, her youngest son, dies in a plane crash
1984, June: in an attempt to crush the secessionist movement in Punjab, she launched "Operation Blue Star". She sent troops into the "Golden Temple" of Amritsar. This led to the death of Jarnail Singh Bindrawale, the leader of the secessionist movement of Sikh militants.

Books on Indira Gandhi:
Indira Gandhi: The Life of Indira Nehru Gandhi
-by Katherine Frank
Indira Gandhi, the 'Emergency', and Indian Democracy
- by P. N. Dhar
Indira Gandhi, Speeches and Writings.
- by Indira Gandhi
The assassination of Indira Gandhi
- by Ritu Sarin
Indira Gandhi : Letters to an American Friend, 1950-1984
- by Dorothy Norman
Indira Gandhi and Foreign Policy Making : The Bangladesh Crisis
- by Narottam Gaan
Indira : a biography of Prime Minister Gandhi
- by Krishan Bhatia
Impact of Indira Gandhi on Indian Political System
- by Dhrub Dumar
Indira Gandhi : Daughter of India (Lerner Biographies)
- by Carol Dommermuth-Costa

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रामाक्रिशाना paramhans

2007-08-14T01:50:00.000-07:00
Ramakrishna Paramahamsa (1836-1886)
Bhagavan Sri Ramakrishna Paramahamsa was born on February 18, 1836. He was a Bengali religious leader. He was a devotee of the Goddess Kali. As a young man he became a temple priest. He immersed himself in intense meditation and other spiritual practices. He became a teacher of Advaita Vedanta Hinduism. He placed “Spiritual Religion” above “Blind Ritualism”.

In his thirst for the divine, Ramakrishna followed different religious paths including various branches of Hinduism. But finally he reached to conclusion that all religions lead to the same goal. Ramakrishna said that his experience of nirvikalpa Samadhi convinced him that the Gods of various religions are merely so many interpretations of the Absolute and that the ultimate reality could never be expressed in human terms. Through many of his Sikh devotees he learned of their faith and its great founders. This exposure to Sikhism and Buddhism further confirmed his experience of the Universality of spiritual truth.

Ramakrishna also believed that his experience of nirvikalpa Samadhi gave him an understanding of the two sides of maya (illusion) which are avidyamaya and vidyamaya. Avidyamaya represents the dark forces of creation which keep the world system on lower planes of consciousness. Vidyamaya, on the other hand, represents the higher forces of creation which elevate human beings to the higher planes of consciousness. With the help of vidyamaya, the devotees can achieve the ultimate goal of becoming mayatita, which means free from maya.

He revitalized Hinduism which had been fraught with excessive ritualism and superstition in the nineteenth century and helped it better respond to challenges from Islam, Christianity, and the dawn of the modern era. The four key concepts in Ramakrishna’s teachings were the following:

The oneness of existence
The divinity of human beings
The unity of God
The harmony of religions

The Ramakrishna Mission was founded by Swami Vivekananda, but it was his spiritual master, Ramakrishna, who directly provided the main impetus for this movement. Although the Brahmo Samaj and the Arya Samaj preceded the Ramakrishna Mission, their influence on a larger level was limited. The life and teachings of this Man of God have had a tremendous impact on the world at large as well as on the people of India.

Among his many other noteworthy characteristics were his universality and child-like purity, intense sincerity, his vast knowledge of thins spiritual and human, and his extraordinary power to transform lives.

His whole life was literally an uninterrupted contemplation of God. He reached a depth of God-consciousness that transcends all time and place and has a universal appeal. Through his Godly life Sri Ramakrishna proved that the revelation of God takes place at all times and that realizing God is not the monopoly of any particular age, or people. In him deepest spirituality and broadest catholicity stood side by side. In the present day world, threatened by nuclear war and torn by religious intolerance, Ramakrishna’s message of harmony gives us hope and shows the right way.

Sayings of Sri Ramakrishna:

I tell you the truth: there is nothing wrong in your being in the world. But you must direct your mind towards God.

There is one whom you may call your own, and that is God.

Money can fetch you bread alone. Do not consider it as your sole end and aim.

You see many stars in the sky at night, but not when the sun rises. Can you therefore say that there are no stars in the heavens during the day? O, man because you cannot find God in the days of your ignorance, say not there is no God.

Seekest thou God? Then seek him in man! His Divinity is manifest more in man than in any other object. Man is greatest manifestation of God.

Women naturally whether good or not, whether chaste or unchaste, should always be regarded as images of the Blissful Divine Mother.

The ego that asserts, ‘I am the servant of God’ is the characteristic of the true devotee. It is the ego of vidya (knowledge), and is called the ‘ripe’ ego.

Let me be condemned to be born over and over again, even in the form of a dog, if so I can be of help to a single soul.

To become great, one must be humble. The tree laden with fruit always bends low. So if you wish to be great, be lowly and meek.

If you say, ‘I am a sinner’, eternally, you will remain a sinner to all eternity. You ought to rather repeat, ‘I am not bound. I am not bound. Who can bind me? I am the son of God, the King of Kings’.

www.piyushdadriwala.4t.com

अटल बिहारी .....

2007-08-14T01:49:00.001-07:00
Atal Bihari Vajpayee
Atal Bihari Vajpayee's political career stretches over 50 years. Over the course of his career, he was elected to the Lok Sabha (House of the People) nine times and twice to the Raj Sabha (House of the Lords). And he twice served as the Prime Minister of India. The first time he served as a Prime Minister, it was for a short time between May 16 and May 31, 1996. The BJP had won the largest number of parliamentary seats in 1996 elections but they failed to form a coalition and therefore, Vajpayee had to resign. However, he became the Prime Minister again on October 13, 1999 when the Bharitiya Janata Party (BJP) won the most number of seats in the parliament and he headed a coalition government---the National Democratic Alliance (NDA).

He began to be seriously interested in politics from his college days when he was a student of Law and Political Science. He then went on to participate in the Quit India Movement and a career in journalism. But his career in journalism lasted only till 1951 when he joined the Bharatiya Jana Sangh (BJS).

The BJS was the precursor of the BJP. In 1957, he was elected to the second Lok Sabha. Over the decades, he was an active member of the Lok Sabha and the Raj Sabha. He also became the leader of the BJS and eventually the BJP too. In 1994, he was given Pt. Govind Ballabh Pant Award for the Best Parliamentarian.

Over the course of his political career, he managed to establish his reputation as a man of the masses, a poet and an inspiring orator. After becoming the Prime Minister, he seemed to have softened BJP's reputation of being anti-muslim. He advocates the development of India as a nuclear power as he supported nuclear tests in Pokran in 1998. He pressed for the continuation of free market reforms and encouraged women's rights.

In 1994, he was conferred the highest civilian award---the Padma Bhushan award.

Some of the titles of the books that he published are:

Lok Sabha Mein Atalji (a collection of speeches)
Mrityu Ya Hatya, Amar Balidan, Kaidi Kavirai Ki Kundalian (a collection of poems written in jail during Emergency)
New Dimensions of India's Foreign Policy (a collection of speeches delivered as External Affairs Minister during 1977-79)
Jana Sangh Aur Musalman
Three Decades in Parliament (Speeches in three volumes)
Amar Aag Hai(a collection of poems) 1994
Meri Ekyavan Kavitayen
Four Decades in Parliament (English)-4 Volumes of Speeches in Parliament, 1957-95

लाल बहादुर sastri

2007-08-14T01:45:00.000-07:00
Lal Bahadur Shastri (1904-1966)
Lal Bahadur Shastri was born in Moghalsarai, which is also spelt as Mughalsarai, on October 2, 1904. His parents were Sharada Prasad and Ramdulari Devi. Though his parents were Srivatsavas, Shastri dropped his caste identity in his early years. His father died when he was only a year old. His mother with the help of her father took care of the children. Lal Bahadur acquired virtues like boldness, love of adventure, patience, self-control, courtesy, and selflessness in his childhood.

His abandoned his studies to take part in the non-cooperation movement started by Gandhi in 1921. He was given the title ‘Shastri’ at Kashi Vidya Peetha in 1926. During his four years’ stay there, he was very much influenced by the lectures of Dr. Bhagawandas on philosophy. In his later life, Shastri displayed poise in the midst of conflict and confusion which he learnt from his teacher, Bhagawandas.

After coming out from Kashi Vidya Peeth, he became the life-member of The Servants of the People Society which was started by Lala Lajpat Rai in 1921. The aim of the society was to train youth who were prepared to dedicate their lives to the service of the country. Shastri earned the love and affection of Lajpat Rai by his earnestness and hard work. Later he became the President of the society. In 1927, Shastri married Lalitha Devi who was from Mirzalyur.

Lal Bahadur Shastri took a leading role in ‘Salt Satyagraha’ which was intensified by 1930. He also advised people not to pay land revenue and taxes to the British government. He was sent to prison for two and half years for doing so. From this time onwards prison became his second home. He was sent to prison seven times and was forced to spend nine long years in various prisons on different occasions.

Going to prison became a blessing in disguise for him. He spent time reading number of books. He became familiar with the works of western philosophers, revolutionaries, and social reformers. He translated the autobiography of Madam Curie, a French scientist who discovered Radium, into Hindi. He was a ideal prisoner. The greatness of Shastri was that he maintained his self-respect even in prison.

After Independence, he became the Minister of police in the ministry of Govind Vallabh Panth. In 1951, he was appointed as the General Secretary of Lok Sabha before regaining a ministerial post as Railways Minister. He resigned following a rail disaster near Ariyalur. He returned to the Cabinet following the general elections, first as Minister of Transport, and then in 1961, he became the Home Minister.

Nehru died in office on May 27, 1964, and left something of a vaccum.Though eclipsed by such stalwarts of the congress party as Kamaraj, and Morarji Desai, the Finance Minister in Nehru’s government, Shastri emerged as the consensus candidate in the midst of the party warfare. The ruling congress party Shastri unanimously as its leader. He became the Prime Minister on June 9, 1964. He became the Prime Minister of India at a very crucial time in Indian history.

The first problem he had to face after becoming the P.M was the one caused by Pakistan. After the Chinese aggression, when India’s confidence in her strength had been shaken, Pakistan was creating trouble along the borders. But Shastriji would not yield to the wickedness of Pakistan. He first tried to earn the good-will and support from the other nations for India. He attended a meeting of non-aligned nations and explained India’s position. Pakistan was awaiting to swallow Kashmir into its territory. She pushed her forces across the eastern border into the Rann of Kuch in Gujarat in 1965. Shastri faced the problem with great tact. But later there was a large scale invasion of the territory by Pakistani soldiers which lead to the break out of war along the cease-fire line on the Kashmir border. Addressing the Nation on 13th August 1965, Shastri referred to Pakistan threats and said, “Force will be met with force”.

Some big Nations feared that if India won a total victory over Pakistan, it would lower their prestige. The Security Council of the United Nations Organization called on India and Pakistan to stop fighting. On the invitation of Kosygin, the Premier of Soviet Russia, Shastri and Ayub Khan met in Tashkent on January 4, 1966. Shastri wished to give one more chance to Pakistan to live in peace and friendship with India. So he signed the treaty of friendship.

Shastriji had suffered heart attacks twice before and during the period of Pakistan war and the following days his body had to bear a very heavy strain. He signed the Joint Declaration on 10th January 1966. He died the same night. Gone was the war hero and the messenger of peace, gone was the great statesman who restored to India her honor and self-respect in the assembly of nations. A tiny, tidy figure. A soul that had lived in perfect purity of thought, word, and deed. Such was this man who had lived in our midst. He belongs to the race of heroes of India.

He was posthumously awarded the Bharat Ratna and a memorial was built for him in Delhi. The slogan, ‘Jai jawan, Jai kisan’ is attributed to Shastri. Lal Bahadur Shastri was a star of great brightness in the history of India.

राजीव gandhi

2007-08-14T01:39:00.000-07:00
Rajiv Gandhi
Rajiv Gandhi entered politics only after the death of his brother, Sanjay Gandhi, in 1980. Rajiv Gandhi had not shown much interest in politics till then. He attended college at Cambridge, England; married an Italian, Sonia Gandhi; and worked as a pilot for the Indian Airlines.

Rajiv's mother, Indira Gandhi, was active in India's national politics as she had by then served as the Prime Minister of India. Rajiv Gandhi's brother was an aide to their mother in politics. So when Sanjay Gandhi died, it is said that Indira Gandhi convinced Rajiv Gandhi to enter politics. But Rajiv Gandhi was not new to politics as he was born into a family of politicians. His grandfather, Nehru, was the first Prime Minister of India. His mother, father and brother too were politically very active.

Rajiv Gandhi won his first parliamentary elections to the Lok Sabha in 1981. At that time, Indira Gandhi was re-elected as the Prime Minister and Rajiv Gandhi became her unofficial political advisor. But in 1984, Indira Gandhi's bodyguards assassinated her and Rajiv Gandhi took over as the head of the Congress party and was sworn in as the Prime Minister.

His government encouraged foreign investment, and industry boomed with the loosening of business controls. He sought to increase Indian investments in modern technology. He removed many restrictions on imports and encouraged foreign investment. His critics claim that he was indecisive as he changed his cabinet members frequently. He fired his mother's aides and instead appointed his friends and technocrats. In 1987, he committed the Indian Peace Keeping Force (IPKF) to Sri Lanka in an endeavor to help the government there eradicate militants agitating for a separate Tamil homeland. Though one of the campaign promises of the Congress party was to eliminate corruption in politics, Rajiv Gandhi's tenure as Prime Minister was marred by allegations of corruption. He was accused of receiving "kick-backs" from a Swedish company manufacturing Bofors machine-guns.

In elections in November 1989 Gandhi won his seat, but the Congress Party lost its majority and he resigned as prime minister. He and his party's implications in corruption scandals decreased their credibility as a strong party.

Rajiv Gandhi began to campaign again in 1991. It was while he was campaigning in Tamil Nadu in south India that a Tamil sucide bomber took his life. They said that it was revenge for intervening in Sri Lanka's politics.

In 1998, 26 members of a separatist guerrilla group known as the Liberation Tigers of Tamil Eelam were convicted of Gandhi's murder and sentenced to death.

And in 1999, Rajiv Gandhi was posthumously charged with participating in a kickback scheme in a Bofors arms deal.

Quick Look : : Life Line
1944: born in Mumbai
1980: his brother Sanjay dies in a plane crash.
1981: His mother, Indira Gandhi convinces him to join politics.
- he is elected into the parliament
1984: Her bodyguards assassinate Indira Gandhi
- Rajiv Gandhi leads the congress party to a sweeping victory and succeeds his mother as Prime Minister.
1987: sends the Indian Peace Keeping Force to Sri Lanka mediate an end to Tamil-Sinhalese violence there.
1988: Allegations of corruption in the Bofors scam diminish his popularity.
1989: the congress party loses its parliamentary majority and Rajiv Gandhi resigns as Prime Minister
1991: while campaigning for the elections, he is assassinated by a Tamil militant suicide bomber in Tamil Nadu. They said it was their revenge for india's intervention in the civil war in Sri Lanka.
1998: 26 members of the Liberation Tigers of Tamil Elam (a separatist guerilla group) are convicted of Rajiv Gandhi's murder and are sentenced to death
1999: Rajiv Gandhi is posthumously charged with participating in a kickback scheme in a Bofors arms deal.

www.piyushdadriwala.4t.com

पी................ush

2007-08-11T08:00:00.001-07:00
A history of Pi

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A chronology of Pi History Topics Index

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A little known verse of the Bible reads

And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. (I Kings 7, 23)

The same verse can be found in II Chronicles 4, 2. It occurs in a list of specifications for the great temple of Solomon, built around 950 BC and its interest here is that it gives π = 3. Not a very accurate value of course and not even very accurate in its day, for the Egyptian and Mesopotamian values of 25/8 = 3.125 and √10 = 3.162 have been traced to much earlier dates: though in defence of Solomon's craftsmen it should be noted that the item being described seems to have been a very large brass casting, where a high degree of geometrical precision is neither possible nor necessary. There are some interpretations of this which lead to a much better value.

The fact that the ratio of the circumference to the diameter of a circle is constant has been known for so long that it is quite untraceable. The earliest values of π including the 'Biblical' value of 3, were almost certainly found by measurement. In the Egyptian Rhind Papyrus, which is dated about 1650 BC, there is good evidence for 4 (8/9)2 = 3.16 as a value for π.

The first theoretical calculation seems to have been carried out by Archimedes of Syracuse (287-212 BC). He obtained the approximation

223/71 < π < 22/7.

Before giving an indication of his proof, notice that very considerable sophistication involved in the use of inequalities here. Archimedes knew, what so many people to this day do not, that π does not equal 22/7, and made no claim to have discovered the exact value. If we take his best estimate as the average of his two bounds we obtain 3.1418, an error of about 0.0002.

Here is Archimedes' argument.

Consider a circle of radius 1, in which we inscribe a regular polygon of 3 2n-1 sides, with semiperimeter bn, and superscribe a regular polygon of 3 2n-1 sides, with semiperimeter an.

The diagram for the case n = 2 is on the right.

The effect of this procedure is to define an increasing sequence

b1 , b2 , b3 , ...

and a decreasing sequence

a1 , a2 , a3 , ...

such that both sequences have limit π.

Using trigonometrical notation, we see that the two semiperimeters are given by

an = K tan(π/K), bn = K sin(π/K),

where K = 3 2n-1. Equally, we have

an+1 = 2K tan(π/2K), bn+1 = 2K sin(π/2K),

and it is not a difficult exercise in trigonometry to show that

(1/an + 1/bn) = 2/an+1 . . . (1)

an+1bn = (bn+1)2 . . . (2)

Archimedes, starting from a1 = 3 tan(π/3) = 3√3 and b1 = 3 sin(π/3) = 3√3/2, calculated a2 using (1), then b2 using (2), then a3 using (1), then b3 using (2), and so on until he had calculated a6 and b6. His conclusion was that

b6 < π < a6 .

It is important to realise that the use of trigonometry here is unhistorical: Archimedes did not have the advantage of an algebraic and trigonometrical notation and had to derive (1) and (2) by purely geometrical means. Moreover he did not even have the advantage of our decimal notation for numbers, so that the calculation of a6 and b6 from (1) and (2) was by no means a trivial task. So it was a pretty stupendous feat both of imagination and of calculation and the wonder is not that he stopped with polygons of 96 sides, but that he went so far.

For of course there is no reason in principle why one should not go on. Various people did, including:

Ptolemy (c. 150 AD) 3.1416

Zu Chongzhi (430-501 AD) 355/113

al-Khwarizmi (c. 800 ) 3.1416

al-Kashi (c. 1430) 14 places

Viète (1540-1603) 9 places

Roomen (1561-1615) 17 places

Van Ceulen (c. 1600) 35 places

Except for Zu Chongzhi, about whom next to nothing is known and who is very unlikely to have known about Archimedes' work, there was no theoretical progress involved in these improvements, only greater stamina in calculation. Notice how the lead, in this as in all scientific matters, passed from Europe to the East for the millennium 400 to 1400 AD.

Al-Khwarizmi lived in Baghdad, and incidentally gave his name to 'algorithm', while the words al jabr in the title of one of his books gave us the word 'algebra'. Al-Kashi lived still further east, in Samarkand, while Zu Chongzhi, one need hardly add, lived in China.

The European Renaissance brought about in due course a whole new mathematical world. Among the first effects of this reawakening was the emergence of mathematical formulae for π. One of the earliest was that of Wallis (1616-1703)

2/π = (1.3.3.5.5.7. ...)/(2.2.4.4.6.6. ...)

and one of the best-known is

π/4 = 1 - 1/3 + 1/5 - 1/7 + ....

This formula is sometimes attributed to Leibniz (1646-1716) but is seems to have been first discovered by James Gregory (1638- 1675).

These are both dramatic and astonishing formulae, for the expressions on the right are completely arithmetical in character, while π arises in the first instance from geometry. They show the surprising results that infinite processes can achieve and point the way to the wonderful richness of modern mathematics.

From the point of view of the calculation of π, however, neither is of any use at all. In Gregory's series, for example, to get 4 decimal places correct we require the error to be less than 0.00005 = 1/20000, and so we need about 10000 terms of the series. However, Gregory also showed the more general result

tan-1 x = x - x3/3 + x5/5 - ... (-1 x 1) . . . (3)

from which the first series results if we put x = 1. So using the fact that

tan-1(1/√3) = π/6 we get

π/6 = (1/√3)(1 - 1/(3.3) + 1/(5.3.3) - 1/(7.3.3.3) + ...

which converges much more quickly. The 10th term is 1/(19 39√3), which is less than 0.00005, and so we have at least 4 places correct after just 9 terms.

An even better idea is to take the formula

π/4 = tan-1(1/2) + tan-1(1/3) . . . (4)

and then calculate the two series obtained by putting first 1/2 and the 1/3 into (3).

Clearly we shall get very rapid convergence indeed if we can find a formula something like

π/4 = tan-1(1/a) + tan-1(1/b)

with a and b large. In 1706 Machin found such a formula:

π/4 = 4 tan-1(1/5) - tan-1(1/239) . . . (5)

Actually this is not at all hard to prove, if you know how to prove (4) then there is no real extra difficulty about (5), except that the arithmetic is worse. Thinking it up in the first place is, of course, quite another matter.

With a formula like this available the only difficulty in computing π is the sheer boredom of continuing the calculation. Needless to say, a few people were silly enough to devote vast amounts of time and effort to this tedious and wholly useless pursuit. One of them, an Englishman named Shanks, used Machin's formula to calculate π to 707 places, publishing the results of many years of labour in 1873. Shanks has achieved immortality for a very curious reason which we shall explain in a moment.
Here is a summary of how the improvement went:

1699: Sharp used Gregory's result to get 71 correct digits

1701: Machin used an improvement to get 100 digits and the following used his methods:

1719: de Lagny found 112 correct digits

1789: Vega got 126 places and in 1794 got 136

1841: Rutherford calculated 152 digits and in 1853 got 440

1873: Shanks calculated 707 places of which 527 were correct

A more detailed Chronology is available.

Shanks knew that π was irrational since this had been proved in 1761 by Lambert. Shortly after Shanks' calculation it was shown by Lindemann that π is transcendental, that is, π is not the solution of any polynomial equation with integer coefficients. In fact this result of Lindemann showed that 'squaring the circle' is impossible. The transcendentality of π implies that there is no ruler and compass construction to construct a square equal in area to a given circle.

Very soon after Shanks' calculation a curious statistical freak was noticed by De Morgan, who found that in the last of 707 digits there was a suspicious shortage of 7's. He mentions this in his Budget of Paradoxes of 1872 and a curiosity it remained until 1945 when Ferguson discovered that Shanks had made an error in the 528th place, after which all his digits were wrong. In 1949 a computer was used to calculate π to 2000 places. In this and all subsequent computer expansions the number of 7's does not differ significantly from its expectation, and indeed the sequence of digits has so far passed all statistical tests for randomness.

You can see 2000 places of π.

We should say a little of how the notation π arose. Oughtred in 1647 used the symbol d/π for the ratio of the diameter of a circle to its circumference. David Gregory (1697) used π/r for the ratio of the circumference of a circle to its radius. The first to use π with its present meaning was an Welsh mathematician William Jones in 1706 when he states "3.14159 andc. = π". Euler adopted the symbol in 1737 and it quickly became a standard notation.

We conclude with one further statistical curiosity about the calculation of π, namely Buffon's needle experiment. If we have a uniform grid of parallel lines, unit distance apart and if we drop a needle of length k < 1 on the grid, the probability that the needle falls across a line is 2k/π. Various people have tried to calculate π by throwing needles. The most remarkable result was that of Lazzerini (1901), who made 34080 tosses and got

π = 355/113 = 3.1415929

which, incidentally, is the value found by Zu Chongzhi. This outcome is suspiciously good, and the game is given away by the strange number 34080 of tosses. Kendall and Moran comment that a good value can be obtained by stopping the experiment at an optimal moment. If you set in advance how many throws there are to be then this is a very inaccurate way of computing π. Kendall and Moran comment that you would do better to cut out a large circle of wood and use a tape measure to find its circumference and diameter.

Still on the theme of phoney experiments, Gridgeman, in a paper which pours scorn on Lazzerini and others, created some amusement by using a needle of carefully chosen length k = 0.7857, throwing it twice, and hitting a line once. His estimate for π was thus given by

2 0.7857 / π = 1/2

from which he got the highly creditable value of π = 3.1428. He was not being serious!

It is almost unbelievable that a definition of π was used, at least as an excuse, for a racial attack on the eminent mathematician Edmund Landau in 1934. Landau had defined π in this textbook published in Göttingen in that year by the, now fairly usual, method of saying that π/2 is the value of x between 1 and 2 for which cos x vanishes. This unleashed an academic dispute which was to end in Landau's dismissal from his chair at Göttingen. Bieberbach, an eminent number theorist who disgraced himself by his racist views, explains the reasons for Landau's dismissal:-

Thus the valiant rejection by the Göttingen student body which a great mathematician, Edmund Landau, has experienced is due in the final analysis to the fact that the un-German style of this man in his research and teaching is unbearable to German feelings. A people who have perceived how members of another race are working to impose ideas foreign to its own must refuse teachers of an alien culture.

G H Hardy replied immediately to Bieberbach in a published note about the consequences of this un-German definition of π

There are many of us, many Englishmen and many Germans, who said things during the War which we scarcely meant and are sorry to remember now. Anxiety for one's own position, dread of falling behind the rising torrent of folly, determination at all cost not to be outdone, may be natural if not particularly heroic excuses. Professor Bieberbach's reputation excludes such explanations of his utterances, and I find myself driven to the more uncharitable conclusion that he really believes them true.

Not only in Germany did π present problems. In the USA the value of π gave rise to heated political debate. In the State of Indiana in 1897 the House of Representatives unanimously passed a Bill introducing a new mathematical truth.

Be it enacted by the General Assembly of the State of Indiana: It has been found that a circular area is to the square on a line equal to the quadrant of the circumference, as the area of an equilateral rectangle is to the square of one side.
(Section I, House Bill No. 246, 1897)

The Senate of Indiana showed a little more sense and postponed indefinitely the adoption of the Act!

Open questions about the number π

Does each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 each occur infinitely often in π?

Brouwer's question: In the decimal expansion of π, is there a place where a thousand consecutive digits are all zero?

Is π simply normal to base 10? That is does every digit appear equally often in its decimal expansion in an asymptotic sense?

Is π normal to base 10? That is does every block of digits of a given length appear equally often in its decimal expansion in an asymptotic sense?

Is π normal ? That is does every block of digits of a given length appear equally often in the expansion in every base in an asymptotic sense? The concept was introduced by Borel in 1909.

Another normal question! We know that π is not rational so there is no point from which the digits will repeat. However, if π is normal then the first million digits 314159265358979... will occur from some point. Even if π is not normal this might hold! Does it? If so from what point? Note: Up to 200 million the longest to appear is 31415926 and this appears twice.

As a postscript, here is a mnemonic for the decimal expansion of π. Each successive digit is the number of letters in the corresponding word.

How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. All of thy geometry, Herr Planck, is fairly hard...:

3.14159265358979323846264...

You can see more about the history of π in the History topic: Squaring the circle and you can see a Chronology of how calculations of π have developed over the years.

www.piyushdadriwalamaths.co.in

zero

2007-08-11T07:56:00.000-07:00
A history of Zero

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One of the commonest questions which the readers of this archive ask is: Who discovered zero? Why then have we not written an article on zero as one of the first in the archive? The reason is basically because of the difficulty of answering the question in a satisfactory form. If someone had come up with the concept of zero which everyone then saw as a brilliant innovation to enter mathematics from that time on, the question would have a satisfactory answer even if we did not know which genius invented it. The historical record, however, shows quite a different path towards the concept. Zero makes shadowy appearances only to vanish again almost as if mathematicians were searching for it yet did not recognise its fundamental significance even when they saw it.

The first thing to say about zero is that there are two uses of zero which are both extremely important but are somewhat different. One use is as an empty place indicator in our place-value number system. Hence in a number like 2106 the zero is used so that the positions of the 2 and 1 are correct. Clearly 216 means something quite different. The second use of zero is as a number itself in the form we use it as 0. There are also different aspects of zero within these two uses, namely the concept, the notation, and the name. (Our name "zero" derives ultimately from the Arabic sifr which also gives us the word "cipher".)

Neither of the above uses has an easily described history. It just did not happen that someone invented the ideas, and then everyone started to use them. Also it is fair to say that the number zero is far from an intuitive concept. Mathematical problems started as 'real' problems rather than abstract problems. Numbers in early historical times were thought of much more concretely than the abstract concepts which are our numbers today. There are giant mental leaps from 5 horses to 5 "things" and then to the abstract idea of "five". If ancient peoples solved a problem about how many horses a farmer needed then the problem was not going to have 0 or -23 as an answer.

One might think that once a place-value number system came into existence then the 0 as an empty place indicator is a necessary idea, yet the Babylonians had a place-value number system without this feature for over 1000 years. Moreover there is absolutely no evidence that the Babylonians felt that there was any problem with the ambiguity which existed. Remarkably, original texts survive from the era of Babylonian mathematics. The Babylonians wrote on tablets of unbaked clay, using cuneiform writing. The symbols were pressed into soft clay tablets with the slanted edge of a stylus and so had a wedge-shaped appearance (and hence the name cuneiform). Many tablets from around 1700 BC survive and we can read the original texts. Of course their notation for numbers was quite different from ours (and not based on 10 but on 60) but to translate into our notation they would not distinguish between 2106 and 216 (the context would have to show which was intended). It was not until around 400 BC that the Babylonians put two wedge symbols into the place where we would put zero to indicate which was meant, 216 or 21 '' 6.

The two wedges were not the only notation used, however, and on a tablet found at Kish, an ancient Mesopotamian city located east of Babylon in what is today south-central Iraq, a different notation is used. This tablet, thought to date from around 700 BC, uses three hooks to denote an empty place in the positional notation. Other tablets dated from around the same time use a single hook for an empty place. There is one common feature to this use of different marks to denote an empty position. This is the fact that it never occured at the end of the digits but always between two digits. So although we find 21 '' 6 we never find 216 ''. One has to assume that the older feeling that the context was sufficient to indicate which was intended still applied in these cases.

If this reference to context appears silly then it is worth noting that we still use context to interpret numbers today. If I take a bus to a nearby town and ask what the fare is then I know that the answer "It's three fifty" means three pounds fifty pence. Yet if the same answer is given to the question about the cost of a flight from Edinburgh to New York then I know that three hundred and fifty pounds is what is intended.

We can see from this that the early use of zero to denote an empty place is not really the use of zero as a number at all, merely the use of some type of punctuation mark so that the numbers had the correct interpretation.

Now the ancient Greeks began their contributions to mathematics around the time that zero as an empty place indicator was coming into use in Babylonian mathematics. The Greeks however did not adopt a positional number system. It is worth thinking just how significant this fact is. How could the brilliant mathematical advances of the Greeks not see them adopt a number system with all the advantages that the Babylonian place-value system possessed? The real answer to this question is more subtle than the simple answer that we are about to give, but basically the Greek mathematical achievements were based on geometry. Although Euclid's Elements contains a book on number theory, it is based on geometry. In other words Greek mathematicians did not need to name their numbers since they worked with numbers as lengths of lines. Numbers which required to be named for records were used by merchants, not mathematicians, and hence no clever notation was needed.

Now there were exceptions to what we have just stated. The exceptions were the mathematicians who were involved in recording astronomical data. Here we find the first use of the symbol which we recognise today as the notation for zero, for Greek astronomers began to use the symbol O. There are many theories why this particular notation was used. Some historians favour the explanation that it is omicron, the first letter of the Greek word for nothing namely "ouden". Neugebauer, however, dismisses this explanation since the Greeks already used omicron as a number - it represented 70 (the Greek number system was based on their alphabet). Other explanations offered include the fact that it stands for "obol", a coin of almost no value, and that it arises when counters were used for counting on a sand board. The suggestion here is that when a counter was removed to leave an empty column it left a depression in the sand which looked like O.

Ptolemy in the Almagest written around 130 AD uses the Babylonian sexagesimal system together with the empty place holder O. By this time Ptolemy is using the symbol both between digits and at the end of a number and one might be tempted to believe that at least zero as an empty place holder had firmly arrived. This, however, is far from what happened. Only a few exceptional astronomers used the notation and it would fall out of use several more times before finally establishing itself. The idea of the zero place (certainly not thought of as a number by Ptolemy who still considered it as a sort of punctuation mark) makes its next appearance in Indian mathematics.

The scene now moves to India where it is fair to say the numerals and number system was born which have evolved into the highly sophisticated ones we use today. Of course that is not to say that the Indian system did not owe something to earlier systems and many historians of mathematics believe that the Indian use of zero evolved from its use by Greek astronomers. As well as some historians who seem to want to play down the contribution of the Indians in a most unreasonable way, there are also those who make claims about the Indian invention of zero which seem to go far too far. For example Mukherjee in [6] claims:-

... the mathematical conception of zero ... was also present in the spiritual form from 17 000 years back in India.

What is certain is that by around 650AD the use of zero as a number came into Indian mathematics. The Indians also used a place-value system and zero was used to denote an empty place. In fact there is evidence of an empty place holder in positional numbers from as early as 200AD in India but some historians dismiss these as later forgeries. Let us examine this latter use first since it continues the development described above.

In around 500AD Aryabhata devised a number system which has no zero yet was a positional system. He used the word "kha" for position and it would be used later as the name for zero. There is evidence that a dot had been used in earlier Indian manuscripts to denote an empty place in positional notation. It is interesting that the same documents sometimes also used a dot to denote an unknown where we might use x. Later Indian mathematicians had names for zero in positional numbers yet had no symbol for it. The first record of the Indian use of zero which is dated and agreed by all to be genuine was written in 876.

We have an inscription on a stone tablet which contains a date which translates to 876. The inscription concerns the town of Gwalior, 400 km south of Delhi, where they planted a garden 187 by 270 hastas which would produce enough flowers to allow 50 garlands per day to be given to the local temple. Both of the numbers 270 and 50 are denoted almost as they appear today although the 0 is smaller and slightly raised.

We now come to considering the first appearance of zero as a number. Let us first note that it is not in any sense a natural candidate for a number. From early times numbers are words which refer to collections of objects. Certainly the idea of number became more and more abstract and this abstraction then makes possible the consideration of zero and negative numbers which do not arise as properties of collections of objects. Of course the problem which arises when one tries to consider zero and negatives as numbers is how they interact in regard to the operations of arithmetic, addition, subtraction, multiplication and division. In three important books the Indian mathematicians Brahmagupta, Mahavira and Bhaskara tried to answer these questions.

Brahmagupta attempted to give the rules for arithmetic involving zero and negative numbers in the seventh century. He explained that given a number then if you subtract it from itself you obtain zero. He gave the following rules for addition which involve zero:-

The sum of zero and a negative number is negative, the sum of a positive number and zero is positive, the sum of zero and zero is zero.

Subtraction is a little harder:-

A negative number subtracted from zero is positive, a positive number subtracted from zero is negative, zero subtracted from a negative number is negative, zero subtracted from a positive number is positive, zero subtracted from zero is zero.

Brahmagupta then says that any number when multiplied by zero is zero but struggles when it comes to division:-

A positive or negative number when divided by zero is a fraction with the zero as denominator. Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero.

Really Brahmagupta is saying very little when he suggests that n divided by zero is n/0. Clearly he is struggling here. He is certainly wrong when he then claims that zero divided by zero is zero. However it is a brilliant attempt from the first person that we know who tried to extend arithmetic to negative numbers and zero.

In 830, around 200 years after Brahmagupta wrote his masterpiece, Mahavira wrote Ganita Sara Samgraha which was designed as an updating of Brahmagupta's book. He correctly states that:-

... a number multiplied by zero is zero, and a number remains the same when zero is subtracted from it.

However his attempts to improve on Brahmagupta's statements on dividing by zero seem to lead him into error. He writes:-

A number remains unchanged when divided by zero.

Since this is clearly incorrect my use of the words "seem to lead him into error" might be seen as confusing. The reason for this phrase is that some commentators on Mahavira have tried to find excuses for his incorrect statement.

Bhaskara wrote over 500 years after Brahmagupta. Despite the passage of time he is still struggling to explain division by zero. He writes:-

A quantity divided by zero becomes a fraction the denominator of which is zero. This fraction is termed an infinite quantity. In this quantity consisting of that which has zero for its divisor, there is no alteration, though many may be inserted or extracted; as no change takes place in the infinite and immutable God when worlds are created or destroyed, though numerous orders of beings are absorbed or put forth.

So Bhaskara tried to solve the problem by writing n/0 = ∞. At first sight we might be tempted to believe that Bhaskara has it correct, but of course he does not. If this were true then 0 times ∞ must be equal to every number n, so all numbers are equal. The Indian mathematicians could not bring themselves to the point of admitting that one could not divide by zero. Bhaskara did correctly state other properties of zero, however, such as 02 = 0, and √0 = 0.

Perhaps we should note at this point that there was another civilisation which developed a place-value number system with a zero. This was the Maya people who lived in central America, occupying the area which today is southern Mexico, Guatemala, and northern Belize. This was an old civilisation but flourished particularly between 250 and 900. We know that by 665 they used a place-value number system to base 20 with a symbol for zero. However their use of zero goes back further than this and was in use before they introduced the place-valued number system. This is a remarkable achievement but sadly did not influence other peoples.

You can see a separate article about Mayan mathematics.

The brilliant work of the Indian mathematicians was transmitted to the Islamic and Arabic mathematicians further west. It came at an early stage for al-Khwarizmi wrote Al'Khwarizmi on the Hindu Art of Reckoning which describes the Indian place-value system of numerals based on 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. This work was the first in what is now Iraq to use zero as a place holder in positional base notation. Ibn Ezra, in the 12th century, wrote three treatises on numbers which helped to bring the Indian symbols and ideas of decimal fractions to the attention of some of the learned people in Europe. The Book of the Number describes the decimal system for integers with place values from left to right. In this work ibn Ezra uses zero which he calls galgal (meaning wheel or circle). Slightly later in the 12th century al-Samawal was writing:-

If we subtract a positive number from zero the same negative number remains. ... if we subtract a negative number from zero the same positive number remains.

The Indian ideas spread east to China as well as west to the Islamic countries. In 1247 the Chinese mathematician Ch'in Chiu-Shao wrote Mathematical treatise in nine sections which uses the symbol O for zero. A little later, in 1303, Zhu Shijie wrote Jade mirror of the four elements which again uses the symbol O for zero.

Fibonacci was one of the main people to bring these new ideas about the number system to Europe. As the authors of [12] write:-

An important link between the Hindu-Arabic number system and the European mathematics is the Italian mathematician Fibonacci.

In Liber Abaci he described the nine Indian symbols together with the sign 0 for Europeans in around 1200 but it was not widely used for a long time after that. It is significant that Fibonacci is not bold enough to treat 0 in the same way as the other numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 since he speaks of the "sign" zero while the other symbols he speaks of as numbers. Although clearly bringing the Indian numerals to Europe was of major importance we can see that in his treatment of zero he did not reach the sophistication of the Indians Brahmagupta, Mahavira and Bhaskara nor of the Arabic and Islamic mathematicians such as al-Samawal.

One might have thought that the progress of the number systems in general, and zero in particular, would have been steady from this time on. However, this was far from the case. Cardan solved cubic and quartic equations without using zero. He would have found his work in the 1500's so much easier if he had had a zero but it was not part of his mathematics. By the 1600's zero began to come into widespread use but still only after encountering a lot of resistance.

Of course there are still signs of the problems caused by zero. Recently many people throughout the world celebrated the new millennium on 1 January 2000. Of course they celebrated the passing of only 1999 years since when the calendar was set up no year zero was specified. Although one might forgive the original error, it is a little surprising that most people seemed unable to understand why the third millennium and the 21st century begin on 1 January 2001. Zero is still causing problems!

History of Ganit (Mathematics)

2007-08-11T07:50:00.000-07:00
History of Ganit (Mathematics)

Introduction
Ganit (Mathematics) has been considered a very important subject since ancient times. We find very elaborate proof of this in Vedah (which were compiled around 6000 BC). The concept of division, addition et-cetera was used even that time. Concepts of zero and infinite were there. We also find roots of algebra in Vedah. When Indian Beez Ganit reached Arab, they called it Algebra. Algebra was name of the Arabic book that described Indian concepts. This knowledge reached to Europe from there. And thus ancient Indian Beez Ganit is currently referred to as Algebra.

The book Vedang jyotish (written 1000 BC) has mentioned the importance of Ganit as follows-

Meaning: Just as branches of a peacock and jewel-stone of a snake are placed at the highest place of body (forehead), similarly position of Ganit is highest in all the branches of Vedah and Shastras

Famous Jain Mathematician Mahaviracharya has said the following-

Meaning: What is the use of much speaking. Whatever object exists in this moving and nonmoving world, can not be understood without the base of Ganit(Mathematics).

This fact was well known to intellectuals of India that is why they gave special importance to the development of Mathematics, right from the beginning. When this knowledge was negligible in Arab and Europe, India had acquired great achievements.

People from Arab and other countries used to travel to India for commerce. While doing commerce, side by side, they also learnt easy to use calculation methods of India. Through them this knowledge reached to Europe. From time to time many inquisitive foreigners visited India and they delivered this matchless knowledge to their countries. This will not be exaggeration to say that till 12th century India was the World Guru in the area of Mathematics.

The auspicious beginning on Indian Mathematics is in Aadi Granth (ancient/eternal book) Rigved. The history of Indian Mathematics can be divided into 5 parts, as following.

1) Ancient Time (Before 500 BC)

a)Vedic Time (1000 BC-At least 6000 BC)
a)Later Vedic Time (1000 BC-500BC)

2) Pre Middle Time (500 BC- 400 AD)

3) Middle Time or Golden Age (400 AD - 1200 AD)

4) Later Middle Time (1200 AD - 1800 AD)

5) Current Time (After 1800 AD)

1) Ancient Time (Before 500 BC)
Ancient time is very important in the history of Indian Mathematics. In this time different branches of Mathematics, such as Numerical Mathematics; Algebra; Geometrical Mathematics, were properly and strongly established.

There are two main divisions in Ancient Time. Numerical Mathematics developed in Vedic Time and Geometrical Mathematics developed in Later Vedic Time.

1a) Vedic Time (1000 BC-At least 6000 BC)
Numerals and decimals are cleanly mentioned in Vedah (Compiled at lease 6000 BC). There is a Richa in Veda, which says the following-

In the above Richa , Dwadash (12), Treeni (2), Trishat (300) numerals have been used. This indicates the use of writing numerals based on 10.

In this age the discovery of ZERO and "10th place value method"(writing number based on 10) is great contribution to world by India in the arena of Mathematics.

If "zero" and "10 based numbers" were not discovered, it would not have been possible today to write big numbers.

The great scholar of America Dr. G. B. Halsteed has also praised this. Shlegal has also accepted that this is the second greatest achievement of human race after the discovery of Alphabets.

This is not known for certain that who invented "zero" and when. But it has been in use right from the "vedic" time. The importance of "zero" and "10th place value method" is manifested by their wide spread use in today's world. This discovery is the one that has helped science to reach its current status.

In the second section of earlier portion of Narad Vishnu Puran (written by Ved Vyas) describes "mathematics" in the context of Triskandh Jyotish. In that numbers have been described which are ten times of each other, in a sequence (10 to the power n). Not only that in this book, different methods of "mathematics" like Addition, Subtraction, Multiplication, Addition, Fraction, Square, Square root, Cube root et-cetera have been elaborately discussed. Problems based on these have also been solved.

This proves at that time various mathematical methods were not in concept stage, rather those were getting used in a methodical and expanded manner.

"10th place value method" dispersed from India to Arab. From there it got transferred to Western countries. This is the reason that digits from 1-9 are called "hindsa" by the people of Arab. In western countries 0,1,2,3,4,5,6,7,8,9 are called Hindu-Arabic Numerals.

1b) Later Vedic Time (1000 BC - 500 BC)

1b.1) Shulv and Vedang Jyotish Time
Vedi was very important while performing rituals. On the top of "Vedi" different type of geomit(geometry: as you notice this word is derived from a Sanskrit word)) were made. To measure those geometry properly, "geometrical mathematics" was developed. That knowledge was available in form of Shulv Sutras (Shulv Formulae). Shulv means rope. This rope was used in measuring geometry while making vedis.

In that time we had three great formulators-Baudhayan, Aapstamb and Pratyayan. Apart from them Manav, Matrayan, Varah and Bandhul are also famous mathematician of that time.

The following excerpt from "Baudhayan Sulv Sutra (1000 BC)" is today known as Paithogorus Theorem (amazing, isn't it ?)

In the above formula , the following has been said. In a Deerghchatursh (Rectangle) the Chetra (Square) of Rajju (hypotenuse) is equal to sum of squares of Parshvamani (base) and Triyangmani (perpendicular).

In the same book Baudhayan has discussed the method of making a square equal to difference of two squares. He has also described method of making a square shape equal to addition of two squares. He has also mentioned the formula to find the value (upto five decimal places) of a root (square root, cube root ...) a number, according to that the square root of 2 can be found as below-

While Geometric Mathematics was developed for making Vedi in Yagya , in parallel there was a need to find appropriate timing for Yagya. This need led to development of Geotish Shastra (Astrology) In Geotish Shastra (Astrology) they calculated time, position and motion of stars. By reading the book Vedanga Jyotish (At least 1000 BC) we find that astrologers knew about addition, multiplication, subtraction et-cetera. For example please read below-

Meaning: Multiply the date by 11, then add to it the "Bhansh" of "Parv" and then divide it by "Nakshatra" number. In this way the "Nakshtra" of date should be told.

1b.2) Surya Pragyapti Time
We find elaborated description of Mathematics in the Jain literature. In fact the clarity and elaboration by which Mathematics is described in Jain literature, indicates the tendency of Jain philosophy to convey the knowledge to the language and level of common people (This is in deviation to the style of Veda which told the facts indirectly).

Surya Pragyapti and Chandra Pragyapti (At least 500 BC) are two famous scriptures of Jain branch of Ancient India. These describe the use of Mathematics.

Deergha Vritt (ellipse) is clearly described in the book titled Surya Pragyapti. "Deergha Vritt" means the outer circle (Vritta) on a rectangle(Deergha), that was also known as Parimandal.
This is clear that Indians had discovered this at least 150 years before Minmax (150 BC). As this history was not known to the West so they consider Minmax as the first time founder of ellipse.

This is worth mentioning that in the book Bhagvati Sutra (Before 300 BC) the word Parimandal has been used for Deergha Vritt (ellipse). It has been described to have two types 1) Pratarparimandal and 2)Ghanpratarparimandal.

Jain Aacharyas contributed a lot in the development of Mathematics. These gurus have described different branches of mathematics in a very through and interesting manner. They are examples too.

They have described fractions, algebraic equations, series, set theory, logarithm, and exponents .... Under the set theory they have described with examples- finite, infinite, single sets. For logarithm they have used terms like Ardh Aached , Trik Aached, Chatur Aached. These terms mean log base 2, log base 3 and log base 4 respectively. Well before Joan Napier (1550-1617 AD), logarithm had been invented and used in India which is a universal truth.

Buddha literature has also given due importance to Mathematics. They have divided Mathematics under two categories- 1) Garna (Simple Mathematics) and 2)Sankhyan (Higher Mathematics). They have described numbers under three categories-1)Sankheya(countable),2)Asankheya(uncountable) and 3)Anant(infinite). Which clearly indicates that Indian Intellectuals knew "infinite number" very well.

2) Pre Middle Time (500 BC- 400 AD)
This is unfortunate that except for the few pages of the books Vaychali Ganit, Surya Siddhanta and Ganita Anoyog of this time, rest of the writings of this time are lost. From the remainder pages of this time and the literature of Aryabhatt, Brahamgupt et-cetera of Middle Time, we can conclude that in this time too Mathematics underwent sufficient development.

Sathanang Sutra, Bhagvati Sutra and Anoyogdwar Sutra are famous books of this time. Apart from these the book titled Tatvarthaadigyam Sutra Bhashya of Jain philosopher Omaswati (135 BC) and the book titled Tiloyapannati of Aacharya (Guru) Yativrisham (176 BC) are famous writings of this time.

The book titled Vaychali Ganit discusses in detail the following -the basic calculations of mathematics, the numbers based on 10, fraction, square, cube, rule of false position, interest methods, questions on purchase and sale... The book has given the answers of the problems and also described testing methods. Vachali Ganit is a proof of the fact that even at that time (300 BC) India was using various methods of the current Numerical Mathematics. This is noticeable that this book is the only written Hindu Ganit book of this time that was found as a few survived pages in village Vaychat Gram (Peshawar) in 1000 AD.

Sathanang Sutra has mentioned five types of infinite and Anoyogdwar Sutra has mentioned four types of Pramaan (Measure). This Granth(book) has also described permutations and combinations which are termed as Bhang and Vikalp .

This is worth mentioning that in the book Bhagvati Sutra describes the following. From n types taking 1-1,2-2 types together the combinations such made are termed as Akak, Dwik Sanyog and the value of such combinations is mentioned as n(n-1)/2 which is used even today.

Roots of the Modern Trignometry lie in the book titled Surya Siddhanta . It mentions Zya(Sine), Otkram Zya(Versesine), and Kotizya(Cosine). Please remember that the same word (Zia) changed to "Jaib" in Arab. The translation of Jaib in Latin was done as "Sinus". And this "Sinus" became "Sine" later on.

This is worth mentioning that Trikonmiti word is pure Indian and with the time it changed to Trignometry. Indians used Trignometry in deciding the position , motion et-cetera of the spatial planets.

In this time the expansion of Beezganit (When this knowledge reached Arab from India it became Algebra)was revolutionary. The roots of Modern Algebra lie in the book Vaychali Ganit. In this book while describing Isht KarmaIsht Karm "Rule of False" as the origin of expansion of Algebra. Thus Algebra is also gifted to world by Indians

Although almost all ancient countries used quantities of unknown values and using them found the result of Numerical Mathematics. However the the expansion of Beez Ganit (Now known as Alzebra) became possible when right denotion method was developed. The glory for this goes to Indians who for the first time used Sanskrit Alphabet to denote unknown quantities. Infact expansion of Beez Ganit (Now known as Alzebra) became possible when Indians realized that all the calculations of Numerical Mathematics could be done by notations. And that +, - these signs can be used with those notations.

Indians developed rules of addition, subtraction, multiplication with these signs (+,-,x). In this context we can not forget the contribution of great mathematician Brahmgupt (628 AD). He said-

The multiplication of a positive number with a negative number comes out to be a negative number and multiplication of a positive number with a positive number comes out to be a positive number.
He further told:
When a positive number is divided by a positive number the result is a positive number and when a positive number is divided by a negative number or a negative number is divided by a positive number the result is a negative number.

Indians used notations for squares, cube and other exponents of numbers. Those notations are used even today in the mathematics. They gave shape to Beezganit Samikaran(Algebraic Equations). They made rules for transferring the quantities from left to right or right to left in an equation. Right from the 5th century AD, Indians majorly used aforementioned rules.

In the book titled Anoyogdwar Sutra has described some rules of exponents in Beez Ganit (Later the name Algebra became more popular). Please find below a few examples.

Thus it proves that Beez Ganit (Later the name Algebra became more popular) was well expanded by the mathematicians of Pre-middle Time. This was more expanded in the Middle Time.

It is without doubt that like Aank Ganit (Numerical Mathematics) Beez Ganit (Later the name Algebra became more popular) reached Arab from India. Arab mathematician Al-Khowarizmi (780-850 AD) has described topics based on Indian Beez Ganit in his book titled "Algebr". And when it reached Europe it was called Algebra.

As for as other countries are concerned we find that in the golden time of Greece Mathematics there was no sign of Algebra with respect to modern concept of Algebra. In classical period Greece people had ability to solve tough questions of Beez Ganit (Later the name Algebra became more popular) but there all solutions were based on Geometrical Mathematics. For the first time in Greece world, the concept of Beez Ganit (Later the name Algebra became more popular) is described in a books of Diofantus (275 AD). By that time Indians were far ahead. This is worth noting that the shape and form of current Beez Ganit (Later the name Algebra became more popular) is originally Indian.

3) Middle Time or Golden Age 400 AD- 1200 AD)
This period is called golden age of Indian Mathematics. In this time great mathematicians like Aryabhatt, Brahmgupt, Mahaveeracharya, Bhaskaracharya who gave a broad and clear shape to almost all the branches of mathematics which we are using today. The principles and methods which are in form of Sutra(formulae) in Vedas were brought forward with their full potential, in front of the common masses. To respect this time India gave the name "Aryabhatt" to its first space satellite.

The following is the description about great mathematicians and their creations.

Aryabhatt (First) (490 AD)
He was a resident of Patna in India. He has described, in a very crisp and concise manner, the important fundamental principles of Mathematics only in 332 Shlokas. His book is titled Aryabhattiya. In the first two sections of Aryabhattiya, Mathematics is described. In the last two sections of Aryabhattiya, Jyotish (Astrology) is described. In the first section of the book, he has described the method of denoting big decimal numbers by the alphabets.

In the second section of the book Aryabhattiya we find difficult questions from topics such as Numerical Mathematics, Geometrical Mathematics, Trignometry and Beezganit (Algebra). He also worked on indeterminate equations of Beezganit (Later in West it was called Algebra). He was the first to use Vyutkram Zia (Which was later known as Versesine in the West) in Trignometry. He calculated the value of pi correct upto four decimal places.

He was first to find that the sun is stationary and the earth revolves around it. 1100 years later, this fact was accepted by Coppernix of West in 16th century. Galileo was hanged for accepting this.

Bhaskar (First) (600 AD)
He did matchless work on Indeterminate equations. He expanded the work of Aryabhatt in his books titled Mahabhaskariya, Aryabhattiya Bhashya and Laghu Bhaskariya .

Brahmgupt (628 AD)
His famous work is his book titled Brahm-sfut. This book has 25 chapters. In two chapters of the book, he has elaborately described the mathematical principles and methods. He threw light on around 20 processes and behavior of Mathematics. He described the rules of the solving equations of Beezganit (Algebra). He also told the solution of indeterminate equations with two exponent. Later Ailer in 1764 AD and Langrez in 1768 described the same.

Brahmgupt told the method of calculating the volume of Prism and Cone. He also described how to sum a GP Series. He was the first to tell that when we divide any positive or negative number by zero it becomes infinite.

Mahaveeracharya (850 AD)
He wrote the book titled "Ganit Saar Sangraha". This book is on Numerical Mathematics. He has described the currently used method of calculating Least Common Multiple (LCM) of given numbers. The same method was used in Europe later in 1500 AD. He derived formulae to calculate the area of ellipse and quadrilateral inside a circle.

Shridharacharya (850 AD)
He wrote books titled "Nav Shatika", "Tri Shatika", "Pati Ganit". These books are on Numerical Mathematics. His books on Beez Ganit (Algebra) are lost now, but his method of solving quadratic equations is still used. This is method is also called "Shridharacharya Niyam". The great thing is that currently we use the same formula as told by him. His book titled "Pati Ganit" has been translated into Arabic by the name "Hisabul Tarapt".

Aryabhatta Second (950 AD)
He wrote a book titled Maha Siddhanta. This book discusses Numerical Mathematics (Ank Ganit) and Algebra. It describes the method of solving algebraic indeterminate equations of first order. He was the first to calculate the surface area of a sphere. He used the value of pi as 22/7.

Shripati Mishra (1039 AD)
He wrote the books titled Siddhanta Shekhar and Ganit Tilak. He worked mainly on permutations and combinations. Only first section of his book Ganit Tilak is available.

Nemichandra Siddhanta Chakravati (1100 AD)
His famous book is titled Gome-mat Saar. It has two sections. The first section is Karma Kaand and the second section is titled Jeev Kaand. He worked on Set Theory. He described universal sets, all types of mapping, Well Ordering Theorems et-cetera.One to One Mapping was used by Gailileo and George Kanter(1845-1918) after many centuries.

Bhaskaracharya Second (1114 AD)
He has written excellent books namely Siddhanta Shiromani,Leelavati Beezganitam,Gola Addhaya,Griha Ganitam and Karan Kautoohal. He gave final touch to Numerical Mathematics, Beez Ganit (Algebra), and Trikonmiti (Trignometry).

The concepts which were in the form of formulae in Vedah. He has also described 20 methods and 8 behaviors of Brahamgupt.

Great Hankal has praised a lot Bhaskaracharya's Chakrawaat Method of solving indeterminate equations of Beezganit (Algebra). This Bhaskaracharya's Chakrawaat Method was used by Ferment in 1667 to solve indeterminate equations.

In his book Siddhanta Shiromani, he has described in length the concepts of Trignometry. He has described Sine, Cosine, Versesine,... Infinitesimal Calculus and Integration. He wrote that earth has gravitational force.

3) Later Middle Period (1200 AD- 1800 AD)
Not much original work was done after Bhaskaracharya Second. Comments on ancient texts are the main contribution of this period.

In his book (1500 AD), the mathematician Neel Kantha of Kerla has given the following formula to calculate Sine r -

The same formula is given in the Malyalam book Mookti Bhaas. These days this series is called Greygeries Series. The following is a descriptions of the famous mathematicians of this period.

Narayan Pundit (1356 AD)
He wrote the book titled Ganit Kaumidi. This book deals with Permutations and Combinations, Partition of Numbers, Magic Squares.

Neel Kanta (1587 AD)
He wrote the book titled Tagikani Kanti. This book deals with Zeotish Ganit(Astrological Mathematics).

Kamalakar (1608 AD)
He wrote a book titled Siddhanta Tatwa Viveka.

Samraat Jagannath (1731 AD)
He wrote two books titled Samraat Siddhanta and Rekha Ganit (Line Mathematics)

Apart from the above-mentioned mathematicians we have a few more worth mentioning mathematicians. From Kerla we have Madhav (1350-1410 AD). Jyeshta Deva (1500-1610 AD) wrote a book titled Ukti Bhasha. Shankar Paarshav (1500-1560 AD) wrote a book titled Kriya Kramkari.

3) Current Period (1800 AD- Current)
Please find below a list of famous mathematicians and their writings.

Nrisingh Bapudev Shastri (1831 AD)
He wrote books on Geometrical Mathematics, Numerical Mathematics and Trignometry.

Sudhakar Dwivedi (1831 AD)
He wrote books titled Deergha Vritta Lakshan(which means characteristics of ellipse), Goleeya Rekha Ganit(which means sphere line mathematics),Samikaran Meemansa(which means analysis of equations) and Chalan Kalan.

Ramanujam (1889 AD)
Ramanujam is a modern mathematics scholar. He followed the vedic style of writing mathematical concepts in terms of formulae and then proving it. His intellectuality is proved by the fact it took all mettle of current mathematicians to prove a few out of his total 50 theorems.

Swami Bharti Krishnateerthaji Maharaj (1884-1960 AD)
He wrote the book titled Vedic Ganit.
www.piyushdadriwalamaths.co.in

An overview of Indian mathematics

2007-08-11T07:43:00.000-07:00
An overview of Indian mathematics

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Ancient Indian Mathematics index History Topics Index

Version for printing
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It is without doubt that mathematics today owes a huge debt to the outstanding contributions made by Indian mathematicians over many hundreds of years. What is quite surprising is that there has been a reluctance to recognise this and one has to conclude that many famous historians of mathematics found what they expected to find, or perhaps even what they hoped to find, rather than to realise what was so clear in front of them.

We shall examine the contributions of Indian mathematics in this article, but before looking at this contribution in more detail we should say clearly that the "huge debt" is the beautiful number system invented by the Indians on which much of mathematical development has rested. Laplace put this with great clarity:-

The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. the importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius.

We shall look briefly at the Indian development of the place-value decimal system of numbers later in this article and in somewhat more detail in the separate article Indian numerals. First, however, we go back to the first evidence of mathematics developing in India.

Histories of Indian mathematics used to begin by describing the geometry contained in the Sulbasutras but research into the history of Indian mathematics has shown that the essentials of this geometry were older being contained in the altar constructions described in the Vedic mythology text the Shatapatha Brahmana and the Taittiriya Samhita. Also it has been shown that the study of mathematical astronomy in India goes back to at least the third millennium BC and mathematics and geometry must have existed to support this study in these ancient times.

The first mathematics which we shall describe in this article developed in the Indus valley. The earliest known urban Indian culture was first identified in 1921 at Harappa in the Punjab and then, one year later, at Mohenjo-daro, near the Indus River in the Sindh. Both these sites are now in Pakistan but this is still covered by our term "Indian mathematics" which, in this article, refers to mathematics developed in the Indian subcontinent. The Indus civilisation (or Harappan civilisation as it is sometimes known) was based in these two cities and also in over a hundred small towns and villages. It was a civilisation which began around 2500 BC and survived until 1700 BC or later. The people were literate and used a written script containing around 500 characters which some have claimed to have deciphered but, being far from clear that this is the case, much research remains to be done before a full appreciation of the mathematical achievements of this ancient civilisation can be fully assessed.

We often think of Egyptians and Babylonians as being the height of civilisation and of mathematical skills around the period of the Indus civilisation, yet V G Childe in New Light on the Most Ancient East (1952) wrote:-

India confronts Egypt and Babylonia by the 3rd millennium with a thoroughly individual and independent civilisation of her own, technically the peer of the rest. And plainly it is deeply rooted in Indian soil. The Indus civilisation represents a very perfect adjustment of human life to a specific environment. And it has endured; it is already specifically Indian and forms the basis of modern Indian culture.

We do know that the Harappans had adopted a uniform system of weights and measures. An analysis of the weights discovered suggests that they belong to two series both being decimal in nature with each decimal number multiplied and divided by two, giving for the main series ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500. Several scales for the measurement of length were also discovered during excavations. One was a decimal scale based on a unit of measurement of 1.32 inches (3.35 centimetres) which has been called the "Indus inch". Of course ten units is then 13.2 inches which is quite believable as the measure of a "foot". A similar measure based on the length of a foot is present in other parts of Asia and beyond. Another scale was discovered when a bronze rod was found which was marked in lengths of 0.367 inches. It is certainly surprising the accuracy with which these scales are marked. Now 100 units of this measure is 36.7 inches which is the measure of a stride. Measurements of the ruins of the buildings which have been excavated show that these units of length were accurately used by the Harappans in construction.

It is unclear exactly what caused the decline in the Harappan civilisation. Historians have suggested four possible causes: a change in climatic patterns and a consequent agricultural crisis; a climatic disaster such flooding or severe drought; disease spread by epidemic; or the invasion of Indo-Aryans peoples from the north. The favourite theory used to be the last of the four, but recent opinions favour one of the first three. What is certainly true is that eventually the Indo-Aryans peoples from the north did spread over the region. This brings us to the earliest literary record of Indian culture, the Vedas which were composed in Vedic Sanskrit, between 1500 BC and 800 BC. At first these texts, consisting of hymns, spells, and ritual observations, were transmitted orally. Later the texts became written works for use of those practicing the Vedic religion.

The next mathematics of importance on the Indian subcontinent was associated with these religious texts. It consisted of the Sulbasutras which were appendices to the Vedas giving rules for constructing altars. They contained quite an amount of geometrical knowledge, but the mathematics was being developed, not for its own sake, but purely for practical religious purposes. The mathematics contained in the these texts is studied in some detail in the separate article on the Sulbasutras.

The main Sulbasutras were composed by Baudhayana (about 800 BC), Manava (about 750 BC), Apastamba (about 600 BC), and Katyayana (about 200 BC). These men were both priests and scholars but they were not mathematicians in the modern sense. Although we have no information on these men other than the texts they wrote, we have included them in our biographies of mathematicians. There is another scholar, who again was not a mathematician in the usual sense, who lived around this period. That was Panini who achieved remarkable results in his studies of Sanskrit grammar. Now one might reasonably ask what Sanskrit grammar has to do with mathematics. It certainly has something to do with modern theoretical computer science, for a mathematician or computer scientist working with formal language theory will recognise just how modern some of Panini's ideas are.

Before the end of the period of the Sulbasutras, around the middle of the third century BC, the Brahmi numerals had begun to appear.

Here is one style of the Brahmi numerals..

These are the earliest numerals which, after a multitude of changes, eventually developed into the numerals 1, 2, 3, 4, 5, 6, 7, 8, 9 used today. The development of numerals and place-valued number systems are studied in the article Indian numerals.

The Vedic religion with its sacrificial rites began to wane and other religions began to replace it. One of these was Jainism, a religion and philosophy which was founded in India around the 6th century BC. Although the period after the decline of the Vedic religion up to the time of Aryabhata I around 500 AD used to be considered as a dark period in Indian mathematics, recently it has been recognised as a time when many mathematical ideas were considered. In fact Aryabhata is now thought of as summarising the mathematical developments of the Jaina as well as beginning the next phase.

The main topics of Jaina mathematics in around 150 BC were: the theory of numbers, arithmetical operations, geometry, operations with fractions, simple equations, cubic equations, quartic equations, and permutations and combinations. More surprisingly the Jaina developed a theory of the infinite containing different levels of infinity, a primitive understanding of indices, and some notion of logarithms to base 2. One of the difficult problems facing historians of mathematics is deciding on the date of the Bakhshali manuscript. If this is a work which is indeed from 400 AD, or at any rate a copy of a work which was originally written at this time, then our understanding of the achievements of Jaina mathematics will be greatly enhanced. While there is so much uncertainty over the date, a topic discussed fully in our article on the Bakhshali manuscript, then we should avoid rewriting the history of the Jaina period in the light of the mathematics contained in this remarkable document.

You can see a separate article about Jaina mathematics.

If the Vedic religion gave rise to a study of mathematics for constructing sacrificial altars, then it was Jaina cosmology which led to ideas of the infinite in Jaina mathematics. Later mathematical advances were often driven by the study of astronomy. Well perhaps it would be more accurate to say that astrology formed the driving force since it was that "science" which required accurate information about the planets and other heavenly bodies and so encouraged the development of mathematics. Religion too played a major role in astronomical investigations in India for accurate calendars had to be prepared to allow religious observances to occur at the correct times. Mathematics then was still an applied science in India for many centuries with mathematicians developing methods to solve practical problems.

Yavanesvara, in the second century AD, played an important role in popularising astrology when he translated a Greek astrology text dating from 120 BC. If he had made a literal translation it is doubtful whether it would have been of interest to more than a few academically minded people. He popularised the text, however, by resetting the whole work into Indian culture using Hindu images with the Indian caste system integrated into his text.

By about 500 AD the classical era of Indian mathematics began with the work of Aryabhata. His work was both a summary of Jaina mathematics and the beginning of new era for astronomy and mathematics. His ideas of astronomy were truly remarkable. He replaced the two demons Rahu, the Dhruva Rahu which causes the phases of the Moon and the Parva Rahu which causes an eclipse by covering the Moon or Sun or their light, with a modern theory of eclipses. He introduced trigonometry in order to make his astronomical calculations, based on the Greek epicycle theory, and he solved with integer solutions indeterminate equations which arose in astronomical theories.

Aryabhata headed a research centre for mathematics and astronomy at Kusumapura in the northeast of the Indian subcontinent. There a school studying his ideas grew up there but more than that, Aryabhata set the agenda for mathematical and astronomical research in India for many centuries to come. Another mathematical and astronomical centre was at Ujjain, also in the north of the Indian subcontinent, which grew up around the same time as Kusumapura. The most important of the mathematicians at this second centre was Varahamihira who also made important contributions to astronomy and trigonometry.

The main ideas of Jaina mathematics, particularly those relating to its cosmology with its passion for large finite numbers and infinite numbers, continued to flourish with scholars such as Yativrsabha. He was a contemporary of Varahamihira and of the slightly older Aryabhata. We should also note that the two schools at Kusumapura and Ujjain were involved in the continuing developments of the numerals and of place-valued number systems. The next figure of major importance at the Ujjain school was Brahmagupta near the beginning of the seventh century AD and he would make one of the most major contributions to the development of the numbers systems with his remarkable contributions on negative numbers and zero. It is a sobering thought that eight hundred years later European mathematics would be struggling to cope without the use of negative numbers and of zero.

These were certainly not Brahmagupta's only contributions to mathematics. Far from it for he made other major contributions in to the understanding of integer solutions to indeterminate equations and to interpolation formulas invented to aid the computation of sine tables.

The way that the contributions of these mathematicians were prompted by a study of methods in spherical astronomy is described in [25]:-

The Hindu astronomers did not possess a general method for solving problems in spherical astronomy, unlike the Greeks who systematically followed the method of Ptolemy, based on the well-known theorem of Menelaus. But, by means of suitable constructions within the armillary sphere, they were able to reduce many of their problems to comparison of similar right-angled plane triangles. In addition to this device, they sometimes also used the theory of quadratic equations, or applied the method of successive approximations. ... Of the methods taught by Aryabhata and demonstrated by his scholiast Bhaskara I, some are based on comparison of similar right-angled plane triangles, and others are derived from inference. Brahmagupta is probably the earliest astronomer to have employed the theory of quadratic equations and the method of successive approximations to solving problems in spherical astronomy.

Before continuing to describe the developments through the classical period we should explain the mechanisms which allowed mathematics to flourish in India during these centuries. The educational system in India at this time did not allow talented people with ability to receive training in mathematics or astronomy. Rather the whole educational system was family based. There were a number of families who carried the traditions of astrology, astronomy and mathematics forward by educating each new generation of the family in the skills which had been developed. We should also note that astronomy and mathematics developed on their own, separate for the development of other areas of knowledge.

Now a "mathematical family" would have a library which contained the writing of the previous generations. These writings would most likely be commentaries on earlier works such as the Aryabhatiya of Aryabhata. Many of the commentaries would be commentaries on commentaries on commentaries etc. Mathematicians often wrote commentaries on their own work. They would not be aiming to provide texts to be used in educating people outside the family, nor would they be looking for innovative ideas in astronomy. Again religion was the key, for astronomy was considered to be of divine origin and each family would remain faithful to the revelations of the subject as presented by their gods. To seek fundamental changes would be unthinkable for in asking others to accept such changes would be essentially asking them to change religious belief. Nor do these men appear to have made astronomical observations in any systematic way. Some of the texts do claim that the computed data presented in them is in better agreement with observation than that of their predecessors but, despite this, there does not seem to have been a major observational programme set up. Paramesvara in the late fourteenth century appears to be one of the first Indian mathematicians to make systematic observations over many years.

Mathematics however was in a different position. It was only a tool used for making astronomical calculations. If one could produce innovative mathematical ideas then one could exhibit the truths of astronomy more easily. The mathematics therefore had to lead to the same answers as had been reached before but it was certainly good if it could achieve these more easily or with greater clarity. This meant that despite mathematics only being used as a computational tool for astronomy, the brilliant Indian scholars were encouraged by their culture to put their genius into advances in this topic.

A contemporary of Brahmagupta who headed the research centre at Ujjain was Bhaskara I who led the Asmaka school. This school would have the study of the works of Aryabhata as their main concern and certainly Bhaskara was commentator on the mathematics of Aryabhata. More than 100 years after Bhaskara lived the astronomer Lalla, another commentator on Aryabhata.

The ninth century saw mathematical progress with scholars such as Govindasvami, Mahavira, Prthudakasvami, Sankara, and Sridhara. Some of these such as Govindasvami and Sankara were commentators on the text of Bhaskara I while Mahavira was famed for his updating of Brahmagupta's book. This period saw developments in sine tables, solving equations, algebraic notation, quadratics, indeterminate equations, and improvements to the number systems. The agenda was still basically that set by Aryabhata and the topics being developed those in his work.

The main mathematicians of the tenth century in India were Aryabhata II and Vijayanandi, both adding to the understanding of sine tables and trigonometry to support their astronomical calculations. In the eleventh century Sripati and Brahmadeva were major figures but perhaps the most outstanding of all was Bhaskara II in the twelfth century. He worked on algebra, number systems, and astronomy. He wrote beautiful texts illustrated with mathematical problems, some of which we present in his biography, and he provided the best summary of the mathematics and astronomy of the classical period.

Bhaskara II may be considered the high point of Indian mathematics but at one time this was all that was known [26]:-

For a long time Western scholars thought that Indians had not done any original work till the time of Bhaskara II. This is far from the truth. Nor has the growth of Indian mathematics stopped with Bhaskara II. Quite a few results of Indian mathematicians have been rediscovered by Europeans. For instance, the development of number theory, the theory of indeterminates infinite series expressions for sine, cosine and tangent, computational mathematics, etc.

Following Bhaskara II there was over 200 years before any other major contributions to mathematics were made on the Indian subcontinent. In fact for a long time it was thought that Bhaskara II represented the end of mathematical developments in the Indian subcontinent until modern times. However in the second half of the fourteenth century Mahendra Suri wrote the first Indian treatise on the astrolabe and Narayana wrote an important commentary on Bhaskara II, making important contributions to algebra and magic squares. The most remarkable contribution from this period, however, was by Madhava who invented Taylor series and rigorous mathematical analysis in some inspired contributions. Madhava was from Kerala and his work there inspired a school of followers such as Nilakantha and Jyesthadeva.

Some of the remarkable discoveries of the Kerala mathematicians are described in [26]. These include: a formula for the ecliptic; the Newton-Gauss interpolation formula; the formula for the sum of an infinite series; Lhuilier's formula for the circumradius of a cyclic quadrilateral. Of particular interest is the approximation to the value of π which was the first to be made using a series. Madhava's result which gave a series for π, translated into the language of modern mathematics, reads

π R = 4R - 4R/3 + 4R/5 - ...

This formula, as well as several others referred to above, were rediscovered by European mathematicians several centuries later. Madhava also gave other formulae for π, one of which leads to the approximation 3.14159265359.

The first person in modern times to realise that the mathematicians of Kerala had anticipated some of the results of the Europeans on the calculus by nearly 300 years was Charles Whish in 1835. Whish's publication in the Transactions of the Royal Asiatic Society of Great Britain and Ireland was essentially unnoticed by historians of mathematics. Only 100 years later in the 1940s did historians of mathematics look in detail at the works of Kerala's mathematicians and find that the remarkable claims made by Whish were essentially true. See for example [15]. Indeed the Kerala mathematicians had, as Whish wrote:-

... laid the foundation for a complete system of fluxions ...

and these works:-

... abound with fluxional forms and series to be found in no work of foreign countries.

There were other major advances in Kerala at around this time. Citrabhanu was a sixteenth century mathematicians from Kerala who gave integer solutions to twenty-one types of systems of two algebraic equations. These types are all the possible pairs of equations of the following seven forms:

x + y = a, x - y = b, xy = c, x2 + y2 = d, x2 - y2 = e, x3 + y3 = f, and x3 - y3 = g.

For each case, Citrabhanu gave an explanation and justification of his rule as well as an example. Some of his explanations are algebraic, while others are geometric. See [12] for more details.

Now we have presented the latter part of the history of Indian mathematics in an unlikely way. That there would be essentially no progress between the contributions of Bhaskara II and the innovations of Madhava, who was far more innovative than any other Indian mathematician producing a totally new perspective on mathematics, seems unlikely. Much more likely is that we are unaware of the contributions made over this 200 year period which must have provided the foundations on which Madhava built his theories.

Our understanding of the contributions of Indian mathematicians has changed markedly over the last few decades. Much more work needs to be done to further our understanding of the contributions of mathematicians whose work has sadly been lost, or perhaps even worse, been ignored. Indeed work is now being undertaken and we should soon have a better understanding of this important part of the history of mathematics.

"(PIYUSH CONSTANT)

2007-08-11T07:34:00.000-07:00
SUM OF EACH DIGIT REMAINS "9"(PIYUSH CONSTANT)
Fri, 2006-07-21 22:34 — piyushdadriwala
SUM OF EACH DIGIT REMAINS SAME(9),NINE
I AM VERY MUCH FOND OF MATHS ,WHATEVER I AM WRITING HERE IS AMAZING,INTERESTING,LEARN IT,VERY SIMPLE.(FOR ANY NO OF DIGITS)
NOW,I HAVE 25 AND 32, MULTIPLE THEM ,NOW YOU CAN MULTIPLE THEM IN FOUR WAYS LIKE THAT(just changing the position)
25*32=800
52*32=1664
25*23=575
52*23=1196
now substract any bigger to any lower you will always get sum of each digit nine.
1664-1196=468(4+6+8=18=1+8=9)
1664-800=864(8+6+4+18=1+8+=9)
1664-575=1089(1+0+8+9=18=1+8=9)
1196-800=396(3+9+6=18=1+8=9)
1196-575=621(6+2+1=9)
800-575=225(2+2+5=9).
this i called "piyush contant"
with lot of regards
piyushdadriwala
www.piyush-g.741.com
pkgdwala@rediffmail.com
in the next topic"what all GODS HAVE COMMON".

www.piyushdadriwalamaths.co.in

पीयूष creation

2007-08-10T07:59:00.000-07:00
Home

My famous thoughts are:

Without God, A man is reverse of God - (Dog)

Luck is as lock, you have it's key.
Click right, it opens.
Click left, it closes

Who loves, always feel with.

God is one but you are many.

A man is of God, but a mind of a man.

The lines that I love most:

I love East because Sun rises,
I love North, Head is
I love South, Sea is
I love but do not love West because Sun Sets.

In front of eye (I)

I want to be busy, do all the work with shy.
Go here or there or fly
Days going high with cry
In front of eye (I)
All good works as God.
Off and on thou scold.
Says, do your duty with the beauty.
Days going down, months coming high
In front of eye (I)
Keep head, hand and heart in the line
Without fear do your fine offend on you will come on line.
Months going, years coming
In front of eye (I)
I want to be busy all the life. All the doing work put in your feet.
Without hate, with faith
Years have gone, some yet to be.
In front of eye (I).

Piyush Thoughts

The thoughts which came in dream.

To imagine is everything.
Pain is sure in gain.
Make your mouth sweet.
Love is heart, by mind
Love makes the way to God.
Time says: Ti-ght-Me otherwise going.
Present is past in future.
Soul is the only precious thing of this world.
A wise thing before doing, but a mad after
Complete you aim within goal, in the goal, always back clockwise.
God: before dying you, ours. But after dying we yours.
Money makes man miser.
See, then lift good, think, than left bad.
Next day, this day will never come.
Luck is a duck, can fly, swim and walk.
In this world there are lot of yesterdays, not many tomorrows.
Much time required, to be good to be bad a few.
We know God, but God know us or not we don't know.

At last

OH! God lot of sorrow
By sorrow
I keep on always
Learning you
All the day
All the way
I believe on you.
How much!
Perhaps
Thou not know.

My words to others

Love, Laugh & Live Long Life.

नेलसन mandela

2007-08-10T07:54:00.000-07:00
Profile of Nelson Rolihlahla Mandela
Nelson Mandela's greatest pleasure, his most private moment, is watching the sun set with the music of Handel or Tchaikovsky playing.

Locked up in his cell during daylight hours, deprived of music, both these simple pleasures were denied him for decades. With his fellow prisoners, concerts were organised when possible, particularly at Christmas time, where they would sing. Nelson Mandela finds music very uplifting, and takes a keen interest not only in European classical music but also in African choral music and the many talents in South African music. But one voice stands out above all - that of Paul Robeson, whom he describes as our hero.

The years in jail reinforced habits that were already entrenched: the disciplined eating regime of an athlete began in the 1940s, as did the early morning exercise. Still today Nelson Mandela is up by 4.30am, irrespective of how late he has worked the previous evening. By 5am he has begun his exercise routine that lasts at least an hour. Breakfast is by 6.30, when the days newspapers are read. The day s work has begun.

With a standard working day of at least 12 hours, time management is critical and Nelson Mandela is extremely impatient with unpunctuality, regarding it as insulting to those you are dealing with.

When speaking of the extensive travelling he has undertaken since his release from prison, Nelson Mandela says: I was helped when preparing for my release by the biography of Pandit Nehru, who wrote of what happens when you leave jail. My daughter Zinzi says that she grew up without a father, who, when he returned, became a father of the nation. This has placed a great responsibility of my shoulders. And wherever I travel, I immediately begin to miss the familiar - the mine dumps, the colour and smell that is uniquely South African, and, above all, the people. I do not like to be away for any length of time. For me, there is no place like home.

Mandela accepted the Nobel Peace Prize as an accolade to all people who have worked for peace and stood against racism. It was as much an award to his person as it was to the ANC and all South Africa s people. In particular, he regards it as a tribute to the people of Norway who stood against apartheid while many in the world were silent.

We know it was Norway that provided resources for farming; thereby enabling us to grow food; resources for education and vocational training and the provision of accommodation over the years in exile. The reward for all this sacrifice will be the attainment of freedom and democracy in South Africa, in an open society which respects the rights of all individuals. That goal is now in sight, and we have to thank the people and governments of Norway and Sweden for the tremendous role they played.

Personal Tastes

Breakfast of plain porridge, with fresh fruit and fresh milk.
A favourite is the traditionally prepared meat of a freshly slaughtered sheep, and the delicacy Amarhewu (fermented corn-meal).
Biographical Details
Nelson Rolihlahla Mandela was born in a village near Umtata in the Transkei on the 18 July 1918. His father was the principal councillor to the Acting Paramount Chief of Thembuland. After his father s death, the young Rolihlahla became the Paramount Chief s ward to be groomed to assume high office. However, influenced by the cases that came before the Chief s court, he determined to become a lawyer. Hearing the elders stories of his ancestors valour during the wars of resistance in defence of their fatherland, he dreamed also of making his own contribution to the freedom struggle of his people.

After receiving a primary education at a local mission school, Nelson Mandela was sent to Healdtown, a Wesleyan secondary school of some repute where he matriculated. He then enrolled at the University College of Fort Hare for the Bachelor of Arts Degree where he was elected onto the Student's Representative Council. He was suspended from college for joining in a protest boycott. He went to Johannesburg where he completed his BA by correspondence, took articles of clerkship and commenced study for his LLB. He entered politics in earnest while studying in Johannesburg by joining the African National Congress in 1942.

At the height of the Second World War a small group of young Africans, members of the African National Congress, banded together under the leadership of Anton Lembede. Among them were William Nkomo, Walter Sisulu, Oliver R. Tambo, Ashby P. Mda and Nelson Mandela. Starting out with 60 members, all of whom were residing around the Witwatersrand, these young people set themselves the formidable task of transforming the ANC into a mass movement, deriving its strength and motivation from the unlettered millions of working people in the towns and countryside, the peasants in the rural areas and the professionals.

Their chief contention was that the political tactics of the old guard' leadership of the ANC, reared in the tradition of constitutionalism and polite petitioning of the government of the day, were proving inadequate to the tasks of national emancipation. In opposition to the old guard', Lembede and his colleagues espoused a radical African Nationalism grounded in the principle of national self-determination. In September 1944 they came together to found the African National Congress Youth League (ANCYL).

Mandela soon impressed his peers by his disciplined work and consistent effort and was elected to the Secretaryship of the Youth League in 1947. By painstaking work, campaigning at the grassroots and through its mouthpiece Inyaniso' (Truth) the ANCYL was able to canvass support for its policies amongst the ANC membership. At the 1945 annual conference of the ANC, two of the League s leaders, Anton Lembede and Ashby Mda, were elected onto the National Executive Committee (NEC). Two years later another Youth League leader, Oliver R Tambo became a member of the NEC.

Spurred on by the victory of the National Party which won the 1948 all-White elections on the platform of Apartheid, at the 1949 annual conference, the Programme of Action, inspired by the Youth League, which advocated the weapons of boycott, strike, civil disobedience and non-co-operation was accepted as official ANC policy.

The Programme of Action had been drawn up by a sub-committee of the ANCYL composed of David Bopape, Ashby Mda, Nelson Mandela, James Njongwe, Walter Sisulu and Oliver Tambo. To ensure its implementation the membership replaced older leaders with a number of younger men. Walter Sisulu, a founding member of the Youth League was elected Secretary-General. The conservative Dr A.B. Xuma lost the presidency to Dr J.S. Moroka, a man with a reputation for greater militancy. The following year, 1950, Mandela himself was elected to the NEC at national conference.

The ANCYL programme aimed at the attainment of full citizenship, direct parliamentary representation for all South Africans. In policy documents of which Mandela was an important co-author, the ANCYL paid special attention to the redistribution of the land, trade union rights, education and culture. The ANCYL aspired to free and compulsory education for all children, as well as mass education for adults.

When the ANC launched its Campaign for the Defiance of Unjust Laws in 1952, Mandela was elected National Volunteer-in-Chief. The Defiance Campaign was conceived as a mass civil disobedience campaign that would snowball from a core of selected volunteers to involved more and more ordinary people, culminating in mass defiance. Fulfilling his responsibility as Volunteer-in-Chief, Mandela travelled the country organising resistance to discriminatory legislation. Charged and brought to trial for his role in the campaign, the court found that Mandela and his co-accused had consistently advised their followers to adopt a peaceful course of action and to avoid all violence.

For his part in the Defiance Campaign, Mandela was convicted of contravening the Suppression of Communism Act and given a suspended prison sentence. Shortly after the campaign ended, he was also prohibited from attending gatherings and confined to Johannesburg for six months.

During this period of restrictions, Mandela wrote the attorneys admission examination and was admitted to the profession. He opened a practice in Johannesburg, in partnership with Oliver Tambo. In recognition of his outstanding contribution during the Defiance Campaign Mandela had been elected to the presidency of both the Youth League and the Transvaal region of the ANC at the end of 1952, he thus became a deputy president of the ANC itself.

Of their law practice, Oliver Tambo, ANC National Chairman at the time of his death in April 1993, has written:

To reach our desks each morning Nelson and I ran the gauntlet of patient queues of people overflowing from the chairs in the waiting room into the corridors... To be landless (in South Africa) can be a crime, and weekly we interviewed the delegations of peasants who came to tell us how many generations their families had worked a little piece of land from which they were now being ejected... To live in the wrong area can be a crime... Our buff office files carried thousands of these stories and if, when we started our law partnership, we had not been rebels against apartheid, our experiences in our offices would have remedied the deficiency. We had risen to professional status in our community, but every case in court, every visit to the prisons to interview clients, reminded us of the humiliation and suffering burning into our people.

Nor did their professional status earn Mandela and Tambo any personal immunity from the brutal apartheid laws. They fell foul of the land segregation legislation, and the authorities demanded that they move their practice from the city to the back of beyond, as Mandela later put it, miles away from where clients could reach us during working hours. This was tantamount to asking us to abandon our legal practice, to give up the legal service of our people... No attorney worth his salt would easily agree to do that, said Mandela and the partnership resolved to defy the law.

Nor was the government alone in trying to frustrate Mandela s legal practice. On the grounds of his conviction under the Suppression of Communism Act, the Transvaal Law Society petitioned the Supreme Court to strike him off the roll of attorneys. The petition was refused with Mr Justice Ramsbottom finding that Mandela had been moved by a desire to serve his black fellow citizens and nothing he had done showed him to be unworthy to remain in the ranks of an honourable profession.

In 1952 Nelson Mandela was given the responsibility to prepare an organisational plan that would enable the leadership of the movement to maintain dynamic contact with its membership without recourse to public meetings. The objective was to prepare for the contingency of proscription by building up powerful local and regional branches to whom power could be devolved. This was the M-Plan, named after him.

During the early fifties Mandela played an important part in leading the resistance to the Western Areas removals and to the introduction of Bantu Education. He also played a significant role in popularising the Freedom Charter, adopted by the Congress of the People in 1955.

In the late fifties, Mandela s attention turned to the struggles against the exploitation of labour, the pass laws, the nascent Bantustan policy, and the segregation of the open universities. Mandela arrived at the conclusion very early on that the Bantustan policy was a political swindle and an economic absurdity. He predicted, with dismal prescience, that ahead there lay a grim programme of mass evictions, political persecutions, and police terror. On the segregation of the universities, Mandela observed that the friendship and inter-racial harmony that is forged through the admixture and association of various racial groups at the mixed universities constitute a direct threat to the policy of apartheid and baasskap, and that it was to remove that threat that the open universities were being closed to black students.

During the whole of the fifties, Mandela was the victim of various forms of repression. He was banned, arrested and imprisoned. For much of the latter half of the decade, he was one of the accused in the mammoth Treason Trial, at great cost to his legal practice and his political work. After the Sharpeville Massacre in 1960, the ANC was outlawed, and Mandela, still on trial, was detained.

The Treason Trial collapsed in 1961 as South Africa was being steered towards the adoption of the republic constitution. With the ANC now illegal the leadership picked up the threads from its underground headquarters. Nelson Mandela emerged at this time as the leading figure in this new phase of struggle. Under the ANC's inspiration, 1,400 delegates came together at an All-in African Conference in Pietermaritzburg during March 1961. Mandela was the keynote speaker. In an electrifying address he challenged the apartheid regime to convene a national convention, representative of all South Africans to thrash out a new constitution based on democratic principles. Failure to comply, he warned, would compel the majority (Blacks) to observe the forthcoming inauguration of the Republic with a mass general strike. He immediately went underground to lead the campaign. Although fewer answered the call than Mandela had hoped, it attracted considerable support throughout the country. The government responded with the largest military mobilisation since the war, and the Republic was born in an atmosphere of fear and apprehension.

Forced to live apart from his family, moving from place to place to evade detection by the government s ubiquitous informers and police spies, Mandela had to adopt a number of disguises. Sometimes dressed as a common labourer, at other times as a chauffeur, his successful evasion of the police earned him the title of the Black Pimpernel. It was during this time that he, together with other leaders of the ANC constituted a new specialised section of the liberation movement, Umkhonto we Sizwe, as an armed nucleus with a view to preparing for armed struggle. At the Rivonia trial, Mandela explained : "At the beginning of June 1961, after long and anxious assessment of the South African situation, I and some colleagues came to the conclusion that as violence in this country was inevitable, it would be wrong and unrealistic for African leaders to continue preaching peace and non-violence at a time when the government met our peaceful demands with force.

It was only when all else had failed, when all channels of peaceful protest had been barred to us, that the decision was made to embark on violent forms of political struggle, and to form Umkhonto we Sizwe...the Government had left us no other choice."

In 1961 Umkhonto we Sizwe was formed, with Mandela as its commander-in-chief. In 1962 Mandela left the country unlawfully and travelled abroad for several months. In Ethiopia he addressed the Conference of the Pan African Freedom Movement of East and Central Africa, and was warmly received by senior political leaders in several countries. During this trip Mandela, anticipating an intensification of the armed struggle, began to arrange guerrilla training for members of Umkhonto we Sizwe.

Not long after his return to South Africa Mandela was arrested and charged with illegal exit from the country, and incitement to strike.

Since he considered the prosecution a trial of the aspirations of the African people, Mandela decided to conduct his own defence. He applied for the recusal of the magistrate, on the ground that in such a prosecution a judiciary controlled entirely by whites was an interested party and therefore could not be impartial, and on the ground that he owed no duty to obey the laws of a white parliament, in which he was not represented.

Mandela prefaced this challenge with the affirmation: I detest racialism, because I regard it as a barbaric thing, whether it comes from a black man or a white man.

Mandela was convicted and sentenced to five years imprisonment. While serving his sentence he was charged, in the Rivonia Trial, with sabotage. Mandela s statements in court during these trials are classics in the history of the resistance to apartheid, and they have been an inspiration to all who have opposed it. His statement from the dock in the Rivonia Trial ends with these words:

I have fought against white domination, and I have fought against black domination. I have cherished the ideal of a democratic and free society in which all persons live together in harmony and with equal opportunities. It is an ideal which I hope to live for and to achieve. But if needs be, it is an ideal for which I am prepared to die.

Mandela was sentenced to life imprisonment and started his prison years in the notorious Robben Island Prison, a maximum security prison on a small island 7Km off the coast near Cape Town. In April 1984 he was transferred to Pollsmoor Prison in Cape Town and in December 1988 he was moved the Victor Verster Prison near Paarl from where he was eventually released. While in prison, Mandela flatly rejected offers made by his jailers for remission of sentence in exchange for accepting the bantustan policy by recognising the independence of the Transkei and agreeing to settle there. Again in the 'eighties Mandela rejected an offer of release on condition that he renounce violence. Prisoners cannot enter into contracts. Only free men can negotiate, he said.
Click image for map

Released on 11 February 1990, Mandela plunged wholeheartedly into his life's work, striving to attain the goals he and others had set out almost four decades earlier. In 1991, at the first national conference of the ANC held inside South Africa after being banned for decades, Nelson Mandela was elected President of the ANC while his lifelong friend and colleague, Oliver Tambo, became the organisation's National Chairperson.

Nelson Mandela has never wavered in his devotion to democracy, equality and learning. Despite terrible provocation, he has never answered racism with racism. His life has been an inspiration, in South Africa and throughout the world, to all who are oppressed and deprived, to all who are opposed to oppression and deprivation.

In a life that symbolises the triumph of the human spirit over man s inhumanity to man, Nelson Mandela accepted the 1993 Nobel Peace Prize on behalf of all South Africans who suffered and sacrificed so much to bring peace to our land.

--------------------------------------------------------------------------------

A Brief Biography
Mandela's words, "The struggle is my life," are not to be taken lightly.

Nelson Mandela personifies struggle. He is still leading the fight against apartheid with extraordinary vigour and resilience after spending nearly three decades of his life behind bars. He has sacrificed his private life and his youth for his people, and remains South Africa's best known and loved hero.

Mandela has held numerous positions in the ANC: ANCYL secretary (1948); ANCYL president (1950); ANC Transvaal president (1952); deputy national president (1952) and ANC president (1991).

He was born at Qunu, near Umtata on 18 July 1918.

His father, Henry Mgadla Mandela, was chief councillor to Thembuland's acting paramount chief David Dalindyebo. When his father died, Mandela became the chief's ward and was groomed for the chieftainship.

Mandela matriculated at Healdtown Methodist Boarding School and then started a BA degree at Fort Hare. As an SRC member he participated in a student strike and was expelled, along with the late Oliver Tambo, in 1940. He completed his degree by correspondence from Johannesburg, did articles of clerkship and enrolled for an LLB at the University of the Witwatersrand.

In 1944 he helped found the ANC Youth League, whose Programme of Action was adopted by the ANC in 1949.

Mandela was elected national volunteer-in-chief of the 1952 Defiance Campaign. He travelled the country organising resistance to discriminatory legislation.

He was given a suspended sentence for his part in the campaign. Shortly afterwards a banning order confined him to Johannesburg for six months. During this period he formulated the "M Plan", in terms of which ANC branches were broken down into underground cells.

By 1952 Mandela and Tambo had opened the first black legal firm in the country, and Mandela was both Transvaal president of the ANC and deputy national president.

A petition by the Transvaal Law Society to strike Mandela off the roll of attorneys was refused by the Supreme Court.

In the 'fifties, after being forced through constant bannings to resign officially from the ANC, Mandela analysed the Bantustan policy as a political swindle. He predicted mass removals, political persecutions and police terror.

For the second half of the 'fifties, he was one of the accused in the Treason Trial. With Duma Nokwe, he conducted the defence.

When the ANC was banned after the Sharpeville massacre in 1960, he was detained until 1961 when he went underground to lead a campaign for a new national convention.

Umkhonto we Sizwe (MK), the military wing of the ANC, was born the same year. Under his leadership it launched a campaign of sabotage against government and economic installations.

In 1962 Mandela left the country for military training in Algeria and to arrange training for other MK members.

On his return he was arrested for leaving the country illegally and for incitement to strike. He conducted his own defence. He was convicted and jailed for five years in November 1962. While serving his sentence, he was charged, in the Rivonia trial, with sabotage and sentenced to life imprisonment.

A decade before being imprisoned, Mandela had spoken out against the introduction of Bantu Education, recommending that community activists "make every home, every shack or rickety structure a centre of learning".

Robben Island, where he was imprisoned, became a centre for learning, and Mandela was a central figure in the organised political education classes.

In prison Mandela never compromised his political principles and was always a source of strength for the other prisoners.

During the 'seventies he refused the offer of a remission of sentence if he recognised Transkei and settled there.

In the 'eighties he again rejected PW Botha's offer of freedom if he renounced violence.

It is significant that shortly after his release on Sunday 11 February 1990, Mandela and his delegation agreed to the suspension of armed struggle.

Mandela has honorary degrees from more than 50 international universities and is chancellor of the University of the North.

He was inaugurated as the first democratically elected State President of South Africa on 10 May 1994 - June 1999

Nelson Mandela retired from Public life in June 1999. He currently resides in his birth place - Qunu, Transkei.

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2007-08-06T07:17:00.000-07:00
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Mathematics (colloquially, maths, or math in American English) is the body of knowledge centered on concepts such as quantity, structure, space, and change, and the academic discipline which studies them; Benjamin Peirce called it "the science that draws necessary conclusions".[1] It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.[2] Knowledge and use of basic mathematics have always been an inherent and integral part of individual and group life. Refinements of the basic ideas are visible in ancient mathematical texts originating in ancient Egypt, Mesopotamia, Ancient India, and Ancient China with increased rigour later introduced by the ancient Greeks. From this point on, the development continued in short bursts until the Renaissance period of the 16th century where mathematical innovations interacted with new scientific discoveries leading to an acceleration in understanding that continues to the present day.[3] Today, mathematics is used throughout the world in many fields, including science, engineering, medicine and economics. The application of mathematics to such fields, often dubbed applied mathematics, inspires and makes use of new mathematical discoveries and has sometimes led to the development of entirely new disciplines. Mathematicians also engage in pure mathematics for its own sake without having any practical application in mind, although applications for what begins as pure mathematics are often discovered later.[4]
EtymologyThe word "mathematics" (Greek: μαθηματικά) comes from the Greek μάθημα (máthēma), which means learning, study, science, and additionally came to have the narrower and more technical meaning "mathematical study", even in Classical times. Its adjective is μαθηματικός (mathēmatikós), related to learning, or studious, which likewise further came to mean mathematical. In particular, μαθηματικὴ τέχνη (mathēmatikḗ tékhnē), in Latin ars mathematica, meant the mathematical art. The apparent plural form in English, like the French plural form les mathématiques (and the less commonly used singular derivative la mathématique), goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural τα μαθηματικά (ta mathēmatiká), used by Aristotle, and meaning roughly "all things mathematical".[5] Despite the form and etymology, the word mathematics, like the names of arts and sciences in general, is used as a singular mass noun in English today. The colloquial English-language shortened forms perpetuate this singular/plural idiosyncrasy, as the word is shortened to math in North American English, while it is maths elsewhere (including Britain, Ireland, Australia and other Commonwealth countries).
History

A quipu, a counting device used by the Inca.
Main article: History of mathematicsThe evolution of mathematics might be seen to be an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges have something in common was a breakthrough in human thought. In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time — days, seasons, years. Arithmetic (addition, subtraction, multiplication and division), naturally followed. Monolithic monuments testify to knowledge of geometry. Further steps need writing or some other system for recording numbers such as tallies or the knotted strings called quipu used by the Inca empire to store numerical data. Numeral systems have been many and diverse. From the beginnings of recorded history, the major disciplines within mathematics arose out of the need to do calculations relating to taxation and commerce, to understand the relationships among numbers, to measure land, and to predict astronomical events. These needs can be roughly related to the broad subdivision of mathematics, into the studies of quantity, structure, space, and change. Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries have been made throughout history and continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."[6]
Inspiration, pure and applied mathematics, and aesthetics

Sir Isaac Newton (1643-1727), an inventor of infinitesimal calculus.
Main article: Mathematical beautyMathematics arises wherever there are difficult problems that involve quantity, structure, space, or change. At first these were found in commerce, land measurement and later astronomy; nowadays, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. Newton was one of the infinitesimal calculus inventors, Feynman invented the Feynman path integral using a combination of reasoning and physical insight, and today's string theory also inspires new mathematics. Some mathematics is only relevant in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. The remarkable fact that even the "purest" mathematics often turns out to have practical applications is what Eugene Wigner has called "the unreasonable effectiveness of mathematics." As in most areas of study, the explosion of knowledge in the scientific age has led to specialization in mathematics. One major distinction is between pure mathematics and applied mathematics. Several areas of applied mathematics have merged with related traditions outside of mathematics and become disciplines in their own right, including statistics, operations research, and computer science. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty also in a clever proof, such as Euclid's proof that there are infinitely many prime numbers, and in a numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics.
Notation, language, and rigor

In modern notation, simple expressions can describe complex concepts. This image is generated by a single equation.
Main article: Mathematical notationMost of the mathematical notation we use today was not invented until the 16th century.[7] Before that, mathematics was written out in words, a painstaking process that limited mathematical discovery. Modern notation makes mathematics much easier for the professional, but beginners often find it daunting. It is extremely compressed: a few symbols contain a great deal of information. Like musical notation, modern mathematical notation has a strict syntax and encodes information that would be difficult to write in any other way. Mathematical language also is hard for beginners. Words such as or and only have more precise meanings than in everyday speech. Also confusing to beginners, words such as open and field have been given specialized mathematical meanings. Mathematical jargon includes technical terms such as homeomorphism and integrable. It was said that Henri Poincaré was only elected to the Académie française so that he could tell them how to define automorphe in their dictionary.[citation needed] But there is a reason for special notation and technical jargon: mathematics requires more precision than everyday speech. Mathematicians refer to this precision of language and logic as "rigor". Rigor is fundamentally a matter of mathematical proof. Mathematicians want their theorems to follow from axioms by means of systematic reasoning. This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.[8] The level of rigor expected in mathematics has varied over time: the Greeks expected detailed arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the definitions used by Newton would lead to a resurgence of careful analysis and formal proof in the 19th century. Today, mathematicians continue to argue among themselves about computer-assisted proofs. Since large computations are hard to verify, such proofs may not be sufficiently rigorous. Axioms in traditional thought were "self-evident truths", but that conception is problematic. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (sufficiently powerful) axiomatic system has undecidable formulas; and so a final axiomatization of mathematics is impossible. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.
Mathematics as science

Carl Friedrich Gauss, while known as the "prince of mathematicians", did not believe that mathematics was worthy of study in its own right[citation needed].Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences".[9] In the original Latin Regina Scientiarum, as well as in German Königin der Wissenschaften, the word corresponding to science means (field of) knowledge. Indeed, this is also the original meaning in English, and there is no doubt that mathematics is in this sense a science. The specialization restricting the meaning to natural science is of later date. If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science. Albert Einstein has stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[10] Many philosophers believe that mathematics is not experimentally falsifiable,[citation needed] and thus not a science according to the definition of Karl Popper. However, in the 1930s important work in mathematical logic showed that mathematics cannot be reduced to logic, and Karl Popper concluded that "most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently."[11] Other thinkers, notably Imre Lakatos, have applied a version of falsificationism to mathematics itself. An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. In fact, the theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics.[12] In any case, mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences. Experimental mathematics continues to grow in importance within mathematics, and computation and simulation are playing an increasing role in both the sciences and mathematics, weakening the objection that mathematics does not use the scientific method. In his 2002 book A New Kind of Science, Stephen Wolfram argues that computational mathematics deserves to be explored empirically as a scientific field in its own right. The opinions of mathematicians on this matter are varied. While some in applied mathematics feel that they are scientists, those in pure mathematics often feel that they are working in an area more akin to logic and that they are, hence, fundamentally philosophers. Many mathematicians feel that to call their area a science is to downplay the importance of its aesthetic side, and its history in the traditional seven liberal arts; others feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science and engineering has driven much development in mathematics. One way this difference of viewpoint plays out is in the philosophical debate as to whether mathematics is created (as in art) or discovered (as in science). It is common to see universities divided into sections that include a division of Science and Mathematics, indicating that the fields are seen as being allied but that they do not coincide. In practice, mathematicians are typically grouped with scientists at the gross level but separated at finer levels. This is one of many issues considered in the philosophy of mathematics. Mathematical awards are generally kept separate from their equivalents in science. The most prestigious award in mathematics is the Fields Medal,[13][14] established in 1936 and now awarded every 4 years. It is usually considered the equivalent of science's Nobel prize. Another major international award, the Abel Prize, was introduced in 2003. Both of these are awarded for a particular body of work, either innovation in a new area of mathematics or resolution of an outstanding problem in an established field. A famous list of 23 such open problems, called "Hilbert's problems", was compiled in 1900 by German mathematician David Hilbert. This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved. A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. Solution of each of these problems carries a $1 million reward, and only one (the Riemann hypothesis) is duplicated in Hilbert's problems.
Fields of mathematics

Early mathematics was entirely concerned with the need to perform practical calculations, as reflected in this Chinese abacus.As noted above, the major disciplines within mathematics first arose out of the need to do calculations in commerce, to understand the relationships between numbers, to measure land, and to predict astronomical events. These four needs can be roughly related to the broad subdivision of mathematics into the study of quantity, structure, space, and change (i.e., arithmetic, algebra, geometry, and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty.
QuantityThe study of quantity starts with numbers, first the familiar natural numbers and integers ("whole numbers") and arithmetical operations on them, which are characterized in arithmetic. The deeper properties of integers are studied in number theory, whence such popular results as Fermat's last theorem. Number theory also holds two widely-considered unsolved problems: the twin prime conjecture and Goldbach's conjecture. As the number system is further developed, the integers are recognised as a subset of the rational numbers ("fractions"). These, in turn, are contained within the real numbers, which are used to represent continuous quantities. Real numbers are generalised to complex numbers. These are the first steps of a hierarchy of numbers that goes on to include quarternions and octonions. Consideration of the natural numbers also leads to the transfinite numbers, which formalise the concept of counting to infinite. Another area of study is size, which leads to the cardinal numbers and then to another conception of infinity: the aleph numbers, which allow meaningful comparison of the size of infinitely large sets.
Natural numbers
Integers
Rational numbers
Real numbers
Complex numbers
StructureMany mathematical objects, such as sets of numbers and functions, exhibit internal structure. The structural properties of these objects are investigated in the study of groups, rings, fields and other abstract systems, which are themselves such objects. This is the field of abstract algebra. An important concept here is that of vectors, generalized to vector spaces, and studied in linear algebra. The study of vectors combines three of the fundamental areas of mathematics: quantity, structure, and space. Vector calculus expands the field into a fourth fundamental area, that of change.

Number theory
Abstract algebra
Group theory
Order theory
SpaceThe study of space originates with geometry - in particular, Euclidean geometry. Trigonometry combines space and number, and encompasses the well-known Pythagorean theorem. The modern study of space generalizes these ideas to include higher-dimensional geometry, non-Euclidean geometries (which play a central role in general relativity) and topology. Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry. Within differential geometry are the concepts of fiber bundles and calculus on manifolds. Within algebraic geometry is the description of geometric objects as solution sets of polynomial equations, combining the concepts of quantity and space, and also the study of topological groups, which combine structure and space. Lie groups are used to study space, structure, and change. Topology in all its many ramifications may have been the greatest growth area in 20th century mathematics, and includes the long-standing Poincaré conjecture and the controversial four color theorem, whose only proof, by computer, has never been verified by a human.

Geometry
Trigonometry
Differential geometry
Topology
Fractal geometry
ChangeUnderstanding and describing change is a common theme in the natural sciences, and calculus was developed as a powerful tool to investigate it. Functions arise here, as a central concept describing a changing quantity. The rigorous study of real numbers and real-valued functions is known as real analysis, with complex analysis the equivalent field for the complex numbers. The Riemann hypothesis, one of the most fundamental open questions in mathematics, is drawn from complex analysis. Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions. One of many applications of functional analysis is quantum mechanics. Many problems lead naturally to relationships between a quantity and its rate of change, and these are studied as differential equations. Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behavior.

Calculus
Vector calculus
Differential equations
Dynamical systems
Chaos theory
Foundations and philosophyIn order to clarify the foundations of mathematics, the fields of mathematical logic and set theory were developed. Mathematical logic is concerned with setting mathematics on a rigid axiomatic framework, and studying the results of such a framework. As such, it is home to Gödel's second incompleteness theorem, perhaps the most widely celebrated result in logic, which (informally) implies that there are always true theorems which cannot be proven. Modern logic is divided into recursion theory, model theory, and proof theory, and is closely linked to theoretical computer science.

Mathematical logic
Set theory
Category theory
Discrete mathematicsDiscrete mathematics is the common name for the fields of mathematics most generally useful in theoretical computer science. This includes computability theory, computational complexity theory, and information theory. Computability theory examines the limitations of various theoretical models of the computer, including the most powerful known model - the Turing machine. Complexity theory is the study of tractability by computer; some problems, although theoretically soluble by computer, are so expensive in terms of time or space that solving them is likely to remain practically unfeasible, even with rapid advance of computer hardware. Finally, information theory is concerned with the amount of data that can be stored on a given medium, and hence concepts such as compression and entropy. As a relatively new field, discrete mathematics has a number of fundamental open problems. The most famous of these is the "P=NP?" problem, one of the Millennium Prize Problems. [15] It is widely believed that the answer to this problem is no. [16]

Combinatorics
Theory of computation
Cryptography
Graph theory
Applied mathematicsApplied mathematics considers the use of abstract mathematical tools in solving concrete problems in the sciences, business, and other areas. An important field in applied mathematics is statistics, which uses probability theory as a tool and allows the description, analysis, and prediction of phenomena where chance plays a role. Most experiments, surveys and observational studies require the informed use of statistics. (Many statisticians, however, do not consider themselves to be mathematicians, but rather part of an allied group.) Numerical analysis investigates computational methods for efficiently solving a broad range of mathematical problems that are typically too large for human numerical capacity; it includes the study of rounding errors or other sources of error in computation.
Mathematical physics • Analytical mechanics • Mathematical fluid dynamics • Numerical analysis • Optimization • Probability • Statistics • Mathematical economics • Financial mathematics • Game theory • Mathematical biology • Cryptography • Operations research
Common misconceptionsMathematics is not a closed intellectual system, in which everything has already been worked out. There is no shortage of open problems. Pseudomathematics is a form of mathematics-like activity undertaken outside academia, and occasionally by mathematicians themselves. It often consists of determined attacks on famous questions, consisting of proof-attempts made in an isolated way (that is, long papers not supported by previously published theory). The relationship to generally-accepted mathematics is similar to that between pseudoscience and real science. The misconceptions involved are normally based on:
misunderstanding of the implications of mathematical rigor;
attempts to circumvent the usual criteria for publication of mathematical papers in a learned journal after peer review, often in the belief that the journal is biased against the author;
lack of familiarity with, and therefore underestimation of, the existing literature. The case of Kurt Heegner's work shows that the mathematical establishment is neither infallible, nor unwilling to admit error in assessing 'amateur' work. And like astronomy, mathematics owes much to amateur contributors such as Fermat and Mersenne.
Relationship between mathematics and physical realityMathematical concepts and theorems need not correspond to anything in the physical world। Insofar as a correspondence does exist, while mathematicians and physicists may select axioms and postulates that seem reasonable and intuitive, it is not necessary for the basic assumptions within an axiomatic system to be true in an empirical or physical sense. Thus, while most systems of axioms are derived from our perceptions and experiments, they are not dependent on them. Nevertheless, mathematics remains extremely useful for solving real-world problems. This fact led Eugene Wigner to write an essay,
piyushdadriwala

मथ्स formula

2007-08-06T07:01:00.000-07:00
Mensuration
Area of a Triangle, (sides a,b,c).. Area = ( b . c sin A )/ 2
Area of a Triangle , s = (a + b + c)/ 2.. Area = Sqrt (s .(s - a). (s - b). (s - c))
Area of a Circle (r = radius).. Area = π . r 2
Area and Volume of a Cylinder
Area and Volume of a Cone
Area and Volume of a Frustrum of a Cone
Area and Volume of a Sphere
Area and Volume of a Pyramid
Trigonometry...
Definitions...Sin A = Opposite / Hypotenuse = a / c Cosine A = Adjacent / Hypotenuse = b / c Tangent A = Opposite / Adjacent = a / bCosecant A = 1 / sin = c / a Secant A = 1/cosine = b / c Cotangent A = 1/tangent. = b / a Trigonometric Relations...Sin ( - A) = - Sin (A)Cos ( - A) = cos (A)Sin (A) 2 + Cos A 2 = 1 Cos (A) 2 =(1 + Cos (2A) ) /2 Sin (A) 2 =(1 - Cos (2A) ) /2 Sin (A) Cos(A) = Sin (2A) /2 Sin (A + / - B) = Sin (A) Cos(B) +/ - Cos(A) Sin(B) Cos (A + / - B) = Cos (A) Cos(B) - /+ Sin(A) Sin(B) 1 + tan(A) 2 = sec(A) 21 + cot(A) 2 = cosec(A) 2
Hyperbolic Functions
sinh x = (e x - e - x) / 2cosh x = (e x + e - x) / 2tanh x = sinh x / cosh x = (e x - e - x) / (e x + e - x)sech x = 1 / sinh x = 2 / (e x - e - x) cosech x = 1 / cosh x = 2 / (e x + e - x)coth x = cosh x / sinh x = (e x + e - x) / (e x - e - x)
ejx = cos x + j sin xex = cosh x + j sinh xsin x = (e jx - e - jx) /2.jcos x = (e jx + e - ix) /2sin jx = j.sinh xcos jx = cohs x
Quadratic EquationA quadratic equation is generally of the form...
ax2 +b x + c = 0The general solution of this equation is
x = ( - b ± Ö (b2 - 4 a c ) /2a
Expansions
sin x = x / 1 - x3/3! + x 5/5! - x 7 / 7! +
cos x = 1 - x 2/2! + x 4/4! - x 6/6!...
ex = 1 + x / 1 + x2/2! + x3/3! +x 4/4!...
sinh x = x / 1! + x 3/3! + x 5/5! + x7 / 7! +
cosh x = 1 + x 2/2! + x 4/4! +x 6/6!...
log(1+ x ) = x - x 2/2! + x 3/3! - x 4/4! + ...
( x + 1)n = 1 + n . x + n .( n - 1 ) x 2 / 2! + n .( n - 1 ). ( n - 2 ) x3 / 3! + ...(n / r ) x r +... ................................( for x < 1 and all real n; all x, n a positive integer)
Derivatives..
f (x)
f '(x)= df(x) / dx
sin x
cos x
cos x
- sin x
tan x
sec2 x
cotan x
- cosec2 x
sec x
sec x. tan x
cosec x ...
- cosec x. cot x.
sinh x ...
cosh x.
cosh x ...
sinh x.
tanh x ...
sech2 x.
cosech x ...
- coth x cosech x
sech x ...
- tanh x sech x
coth x ...
- cosech 2 x
u .v
u . dv/dx + v . du/dx
u / v
(v . du / dx - u . dv / dx ) / v 2
a. x n
a. n . x n - 1
e a x
a . e a x
a x
a x. ln a
x x
x x /(1 + ln x)
ln x
1 / x
log a x
1 / x . log a e
sin - 1( x /a)
1 / Sqrt(a 2 - x 2 )
cos - 1( x /a)
- 1 / Sqrt(a 2 - x 2 )
tan - 1( x /a)
a / (a 2 + x 2 )
Indefinite Integrals..
f(x)
The constant of integration C is ommitted from the table of indefinite integrals below

xa
x a+1 / (a + 1)

1 / (x 2 + a2)
(1 / a) . tan - 1 (x / a)

1 / (x 2 - a2)
(1 /2 a) . ln ( ( x - a ) /(x + a))

( a + b x ) n (n not - 1)
(a + b x)n + 1 / b (n + 1)

( a + b x ) - 1
1 / b .ln ( a + b x )

x / (a x +b)
(a x + b - b ln(ax +b) ) / a2

1 / x
ln x

1 / Sqrt (x 2 - a 2)
cosh - 1 (x / a)

1 / Sqrt (x 2 + a 2)
sinh - 1 (x / a)

ex
ex

1 / ( a2 - x2)
(1 / a). tanh - 1 ( x / a ) = 1 /( 2. a) . log(a + x/a - x )

ax
ax / ln a

x ax
(a x / ln a ) - (a x /( ln a ) 2 )

x ea x
e a x (a x - 1) / a2

1 /(a + b e c x )
(x / a) - ln (a + b ec x ) / a c

ln x
x (ln x - 1 )

( ln x )2
x [ (ln x )2 - 2 ln x +2 ]

1 / x ln x
ln ( ln x )

sin x
- cos x

cos x
sin x

tan x
- ln cos x

cotan x
ln sin x

sec x
ln ( sec x + tan x ) = ln (tan (x/ 2 + π/ 4) )

cosec x
log tan x/ 2

1 / Sqrt( x 2 + a 2)
sinh - 1( x / a ) = log ( (x/a) +Sqrt(x2 /a2 +1))

1 / Sqrt( x2 - a 2)
cosh - 1( x / a )

1 / Sqrt( a2 - x 2)
sin - 1( x / a )

sinh x
cosh x

cosh x
sinh x

tanh x
ln cosh x

cosech x
ln tanh (x / 2 )

sech x
tan - 1 ( sinh x )

coth x
ln sinh x

sinh 2 x
( - x + ( sinh (2 x)) /2 ) / 2

cosh 2 x
( x + ( sinh (2 x) ) /2 ) / 2

sech 2 x
tanh x

cosech 2 x
- coth x

tanh 2 x
x - tanh x
Moments Of Inertia of Plane SectionsI = moment of Inertia about the identified axis.J = Polar moment of inertia about the centroid of section
For More detailed information refer..
Properties of Plane Areas Properties of solids
Parallel axis Theory.. If the second moment of an area (A) about an axis x - x = I xx. Then the second moment of Area about a parallel axis y - y which is distance x from x - x =
I yy = I xx + A . x 2
Complex Numbers..
In mathematics it is necessary to provide a method of identifying the root of a negative number i.e p = √ ( - 4). p is clearly not real number it is an imaginary number. Again an equation x2 - 2x +5 = 0 results in (x - 1)2 = - 4 so that (x - 1) = ± √ ( - 4). The roots are therefore x = 1 - √ ( - 4), and 1 + √ ( - 4), These roots which are a combination of a real number and an imaginary number are called complex numbers.The symbol i (j in electical work) is used to represent √ - 1. Therefore √ ( - 4) = 2i. The number i, or 1i , or xi are called purely imaginary numbers. The complex number solution of the above equation = and 1 + 2i and 1 - 2i,Powers of complex are identified below
i 1 =
+i

i - 1 =
- i
i 2 =
- 1

i - 2 =
- 1
i 3 =
- i

i - 3 =
+i
i 4 =
+1

i - 4 =
- 1
...
...
i...
...
i 5 =
+i

i - 5 =
- i
etc .
For two complex numbers (a 1 + ib 1) & (a 2 +ib 2)to be equal it can be easily proved that a 1 must equal a 2, and b 1 must equal b 2Complex numbers are conveniently represented using an argand diagrams as shown below.
Complex numbers can be manipulated using the Cartesian system as follows;
z = a + i bz 1 + z 2 = (a 1 + a 2) + i (b 1 + b 2)z 1 - z 2 = (a 1 + a 2) - i (b 1 + b 2)z 1 . z 2 = (a 1 . a 2 - b 1 .b 2) + i (a 1 . b 2 + a 2 .b a)a2 + a2 = r2 = (a +ib) (a - ib)
Complex numbers can be manipulated using the polar co - ordinate system as follows;
z = a + i b = r (cos φ + i। sin φ )r = √(a2 + b2 ),φ = arctan (b/a) = tan - 1 (b/a)sin φ = b/r, cos φ = a/r, tan φ = b/az 1. z 2 = r 1.r 2 [cos (φ 1 + φ 2 ) + i (sin (φ 1 + φ 2 ) ]z n = r n [cos (n φ) + i sin (n φ) ] z > 0 , Integere i φ = cos ( φ) + i sin ( φ ) Eulers formula i φ =ln [ (cos ( φ) + i sin ( φ ) ]e - i φ = cos ( φ) - i sin ( φ ) = 1/ [ cos ( φ) + i sin ( φ ) ].
piyushdadriwala

2007-08-06T06:57:00.000-07:00
Albert Einstein
March 14, 1879 - April 18, 1955Physicist and MathematicianNobel Laureate for Physics 1921
"There are only two ways to live your life. One is as though nothing is a miracle. The other is as if everything is."- Albert Einstein -
Albert Einstein was a German-born theoretical physicist who is widely considered one of the greatest physicists of all time.
While best known for the theory of relativity (and specifically mass-energy equivalence, E=mc2), he was awarded the 1921 Nobel Prize in Physics for his 1905 (Annus Mirabilis) explanation of the photoelectric effect and "for his services to Theoretical Physics". In popular culture, the name "Einstein" has become synonymous with great intelligence and genius. Einstein was named Time magazine's "Man of the Century."
He was known for many scientific investigations, among which were: his special theory of relativity which stemmed from an attempt to reconcile the laws of mechanics with the laws of the electromagnetic field, his general theory of relativity which extended the principle of relativity to include gravitation, relativistic cosmology, capillary action, critical opalescence, classical problems of statistical mechanics and problems in which they were merged with quantum theory, leading to an explanation of the Brownian movement of molecules; atomic transition probabilities, the probabilistic interpretation of quantum theory, the quantum theory of a monatomic gas, the thermal properties of light with a low radiation density which laid the foundation of the photon theory of light, the theory of radiation, including stimulated emission; the construction of a unified field theory, and the geometrization of physics.
Einstein was born on March 14, 1879, to a Jewish family, in Ulm, Württemberg, Germany. His father was Hermann Einstein, a salesman who later ran an electrochemical works, and his mother was Pauline née Koch. They were married in Stuttgart-Bad Cannstatt.
At his birth, Albert's mother was reputedly frightened that her infant's head was so large and oddly shaped. Though the size of his head appeared to be less remarkable as he grew older, it's evident from photographs of Einstein that his head was disproportionately large for his body throughout his life, a trait regarded as "benign macrocephaly" in large-headed individuals with no related disease or cognitive deficits. His parents also worried about his intellectual development as a child due to his initial language delay and his lack of fluency until the age of nine, though he was one of the top students in his elementary school.
In 1880, shortly after Einstein's birth the family moved to Munich, where his father and his uncle founded a company manufacturing electrical equipment (Elektrotechnische Fabrik J. Einstein & Cie). This company provided the first lighting for the Oktoberfest as well as some cabling in the suburb of Schwabing.
Albert's family members were all non-observant Jews and he attended a Catholic elementary school. At the insistence of his mother, he was given violin lessons. Though he initially disliked the lessons, and eventually discontinued them, he would later take great solace in Mozart's violin sonatas.
When Einstein was five, his father showed him a small pocket compass, and Einstein realized that something in "empty" space acted upon the needle; he would later describe the experience as one of the most revelatory events of his life. He built models and mechanical devices for fun and showed great mathematical ability early on.
In 1889, a medical student named Max Talmud (later: Talmey), who regularly visited the Einsteins, introduced Einstein to key science and philosophy texts, including Kant's Critique of Pure Reason.
Einstein attended the Luitpold Gymnasium, where he received a relatively progressive education. In 1891, he taught himself Euclidean geometry from a school booklet and began to study calculus; Einstein realized the power of deductive reasoning from Euclid's Elements, which Einstein called the "holy little geometry book" (given by Max Talmud). At school, Einstein clashed with authority and resented the school regimen, believing that the spirit of learning and creative thought were lost in such endeavors as strict rote learning.
From 1894, following the failure of Hermann Einstein's electrochemical business, the Einsteins moved to Milan and proceeded to Pavia after a few months. Einstein's first scientific work, called "The Investigation of the State of Aether in Magnetic Fields", was written contemporaneously for one of his uncles. Albert remained in Munich to finish his schooling, but only completed one term before leaving the gymnasium in the spring of 1895 to join his family in Pavia. He quit a year and a half before the final examinations, convincing the school to let him go with a medical note from a friendly doctor, but this meant that he had no secondary-school certificate. That same year, at age 16, he performed a famous thought experiment by trying to visualize what it would be like to ride alongside a light beam. He realized that, according to Maxwell's equations, light waves would obey the principle of relativity: the speed of the light would always be constant, no matter what the velocity of the observer. This conclusion would later become one of the two postulates of special relativity.
Rather than pursuing electrical engineering as his father intended for him, he followed the advice of a family friend and applied at the Federal Polytechnic Institute in Zurich in 1895. Without a school certificate he had to take an admission exam, which he - at the age of 16 being the youngest participant did not pass. He had preferred travelling in northern Italy over the required preparations for the exam. Still, he easily passed the science part, but failed in general knowledge.
After that he was sent to Aarau, Switzerland to finish secondary school. He lodged with Professor Jost Winteler's family and became enamoured with Sofia Marie-Jeanne Amanda Winteler, commonly referred to as Sofie or Marie, their daughter and his first sweetheart. Einstein's sister, Maja, who was perhaps his closest confidant, was to later marry their son, Paul. While there, he studied Maxwell's electromagnetic theory and received his diploma in September 1896. Einstein subsequently enrolled at the Federal Polytechnic Institute in October and moved to Zurich, while Marie moved to Olsberg, Switzerland for a teaching post. The same year, he renounced his Württemberg citizenship to avoid military service.
In the spring of 1896, Mileva Maric started as a medical student at the University of Zurich, but after a term switched to the Federal Polytechnic Institute. She was the only woman to study in that year for the same diploma as Einstein. Maric's relationship with Einstein developed into romance over the next few years, though his mother objected because she was too old, not Jewish, and physically defective.
In 1900, Einstein was granted a teaching diploma by the Federal Polytechnic Institute. Einstein then submitted his first paper to be published, on the capillary forces of a straw, titled "Consequences of the observations of capillarity phenomena". In this paper his quest for a unified physical law becomes apparent, which he followed throughout his life. Through his friend Michele Besso, Einstein was presented with the works of Ernst Mach, and would later consider him "the best sounding board in Europe" for physical ideas. Einstein and Maric had a daughter, Lieserl Einstein, born in January 1902. Her fate is unknown; some believe she died in infancy, while others believe she was given out for adoption.
Works and Doctorate
Einstein could not find a teaching post upon graduation, mostly because his brashness as a young man had apparently irritated most of his professors. The father of a classmate helped him obtain employment as a technical assistant examiner at the Swiss Patent Office[8] in 1902. His main responsibility was to evaluate patent applications relating to electromagnetic devices. He also learned how to discern the essence of applications despite sometimes poor descriptions, and was taught by the director how "to express [him]self correctly". He occasionally corrected their design errors while evaluating the practicality of their work.
His friend from Zurich, Michele Besso, also moved to Bern and took a job at the patent office, and he became an important sounding board. Einstein also joined with two friends he made in Bern, Maurice Solovine and Conrad Habicht, to create a weekly discussion club on science and philosophy, which they grandly and jokingly named "The Olympia Academy." Their readings included Poincare, Mach, Hume, and others who influenced the development of the special theory of relativity.
Einstein married Mileva Maric on January 6, 1903. Einstein's marriage to Maric who was a mathematician, was both a personal and intellectual partnership: Einstein referred to Mileva as "a creature who is my equal and who is as strong and independent as I am". Ronald W. Clark, a biographer of Einstein, claimed that Einstein depended on the distance that existed in his marriage to Mileva in order to have the solitude necessary to accomplish his work; he required intellectual isolation. In an obituary of Einstein Abram Joffe wrote: "The author of [the papers of 1905] wasŠ a bureaucrat at the Patent Office in Bern, Einstein-Maric which has been taken as evidence of a collaborative relationship. However, most probably Joffe referred to Einstein- Maric ecause he believed that it was a Swiss custom at the time to append the spouse's surname to the husband's name. The extent of her influence on Einstein's work is a controversial and debated question.
In 1903, Einstein's position at the Swiss Patent Office had been made permanent, though he was passed over for promotion until he had "fully mastered machine technology". He obtained his doctorate under Alfred Kleiner at the University of Zürich after submitting his thesis "A new determination of molecular dimensions" ("Eine neue Bestimmung der Moleküldimensionen") in 1905.
During 1905, in his spare time, he wrote four articles that participated in the foundation of modern physics, without much scientific literature he could refer to or many fellow scientists with whom he could discuss the theories. Most physicists agree that three of those papers (on Brownian motion, the photoelectric effect, and special relativity) deserved Nobel Prizes. Only the paper on the photoelectric effect would be mentioned by the Nobel committee in the award; at the time of the award, it had the most unchallenged experimental evidence behind it, although the Nobel committee expressed the opinion that Einstein's other work would be confirmed in due course.
Some might regard the award for the photoelectric effect ironic, not only because Einstein is far better-known for relativity, but also because the photoelectric effect is a quantum phenomenon, and Einstein became somewhat disenchanted with the path quantum theory would take.
Einstein submitted this series of papers to the "Annalen der Physik". They are commonly referred to as the "Annus Mirabilis Papers" (from Annus mirabilis, Latin for 'year of wonders')।
In the last years of Albert Einstein's life, he amused himself by telling jokes to his parrot, and avoided visitors by feigning illness, according to a newly discovered diary written by the woman known around Princeton as his last girlfriend. While Einstein also talked about the travails of his continuing work in physics, most of Johanna Fantova's diary recalls his views on world politics and his personal life. The writings are an unvarnished portrait of Einstein struggling bravely with the manifold inconveniences of sickness and old age, Freeman Dyson, a mathematician at the Institute for Advanced Study in Princeton, told The New York Times in Saturday¹s editions.
The 62-page diary, written in German, was discovered in February in Fantova¹s personnel files at Princeton University¹s Firestone Library, where she had worked as a curator. The manuscript is the subject of an article to be published next month in The Princeton University Library Journal. According to the article, the new manuscript is the only one kept by someone close to Einstein in the final years of his life.
"There is surprisingly little about physics in the diary," Donald Skemer, Firestone Library¹s curator of manuscripts, told The Times of Trenton. Fantova wrote that she recorded her time with the renowned physicist to "cast some additional light on our understanding of Einstein, not on the great man who became a legend in his lifetime, not on Einstein the renowned scientist, but on Einstein the humanitarian." Fantova was 22 years younger than Einstein. Although the two spent considerable time together starting in the 1940s, her journal only records their relationship from October 1953 until his death in April 1955 at age 76. She died in 1981 at age 80.
Princeton already had a collection of the poems, letters and photos Einstein sent to Fantova, who sold them after his death to Gillett G. Griffin, a retired curator at Princeton¹s Art Museum. He gave those documents to the library. Griffin, invited many times to Einstein¹s home for dinner, said Fantova was a fixture there. "Reading what she left gives me an immediate connection with my own experience and gives everyone the immediacy of knowing Einstein himself," Griffin said.
The diary recounts Einstein speaking about the politics of the day and portrays him as critical of speeches of Adlai Stevenson, the nuclear arms race and the anti-communist attack on the scientist J. Robert Oppenheimer by Sen. Joseph McCarthy. "This political persecution of his associate was a source of bitter disillusionment," Fantova wrote. Besides his politics, Fantova wrote of Einstein's popularity and how he tried to write back to strangers, some of whom tried to convert him to Christianity. He said, "All the maniacs in the world write to me," she wrote.
Lighter moments recounted The diary also recounts how, on his 75th birthday, Einstein received a parrot as gift. After deciding the bird was depressed, Einstein tried alter its mood by telling bad jokes. At times, Einstein would pretend to be sick in bed so he would not have to pose with visitors who wanted photographs. Einstein still enjoyed himself even when real illness did take hold. Einstein¹s health began to fail, but he continued to indulge in what remained his favorite of all pastimes, sailing. Seldom did I see him so gay and in so light a mood as in this strangely primitive little boat, Fantova wrote. Einstein also wrote Fantova poems, some of which are in the diary.
Einstein, with his second wife Elsa, had arrived in Princeton in 1933 at the newly formed Institute for Advanced Study. Elsa died three years later. Fantova first met Einstein in 1929 in Berlin. She arrived in the United States alone in 1939 and, at Einstein¹s urging, attended library school at the University of North Carolina.
ESP lab sees doors close Guardian - February 12, 2007 "A laboratory dedicated to extra-sensory perception and telekinesis at the prestigious Princeton University in New Jersey is to close after nearly 30 years of research."
Einstein the Greatest
November 29, 1999 - BBC
Albert Einstein has been voted the greatest physicist of all time in an end of the millennium poll, pushing Sir Isaac Newton into second place.
The survey was conducted among 100 of today's leading physicists.
All-time top ten:
1. Albert Einstein2. Isaac Newton3. James Clerk Maxwell4. Niels Bohr5. Werner Heisenberg6. Galileo Galilei7. Richard Feynman8. Paul Dirac9. Erwin Schrödinger10. Ernest Rutherford
"Einstein's special and general theories of relativity completely overturned previous conceptions of a universal, immutable space and time, and replaced them with a startling new framework in which space and time are fluid and malleable," said physicist Brian Greene from Columbia University, US, who participated in the poll for Physics World magazine.
Peter Rodgers, Editor of Physics World, said: "Einstein and Newton were always going to be one and two but what was surprising about the top 10 was that there were seven out and out theorists."
The top 10 includes three British scientists: Newton, James Clerk Maxwell and Paul Dirac. New Zealander Ernest Rutherford, who did much of his work in the UK, also makes the list, at 10.
Hawking and Archimedes
A parallel survey of rank-and-file physicists by the site PhysicsWeb gave the top spot to Newton and also included Michael Faraday.
Neither list included any living scientist, but Stephen Hawking was rated at 16 by PhysicsWeb users, just behind Archimedes.
Paul Guinnessy, editor of PhysicsWeb, said: "My two biggest surprises were the inclusion of Stephen Hawking, as I think more time is needed to see whether his scientific contributions will last, and the low number of votes for Marie Curie and Ernest Rutherford.
"Both these physicists had a dramatic impact not only on scientific achievements but in the students they taught and drew into physics. Rutherford's lab in particular had a number of students who were awarded Nobel prizes at a later date."
Big science
The three most important discoveries in physics are quantum mechanics, Einstein's theory of general relativity and Newton's mechanics and gravitation.
Quantum computation pioneer David Deutsch of Oxford University said: "In each of these three cases, the discovery in question not only revolutionised the branch of physics that it nominally addressed, but also provided a framework so deep and universal that all subsequent theories in physics have been formulated within it."
Asked about their careers, the physicists said they were mostly happy. Over 70% of respondents said they would study physics if they were starting university this year. But 17% said they would not, with one Japanese researcher commenting: "I worked too hard. I want to enjoy life next time."
However, asked for the biggest problem in physics, one respondent joked "getting tenure or quantum gravity".
As is traditional, the physicists had a high opinion of their subject, calling it "the most grandiose science", "the most fascinating activity for our brain" and "still the most fundamental of all sciences".
But the biological sciences did appeal to some. Michael Green, a particle theorist at Cambridge University, said: "There is something attractive about a subject that is still in a relatively primitive state."
Einstein's brain found to be anatomically distinct

Einstein allowed his brain to be studied after his death
AP - June 17, 1999
We always thought something must have made Albert Einstein smarter than the rest of us. Now, scientists have found that one part of his brain was indeed physically extraordinary.
In the only study ever conducted of the overall anatomy of Einstein's brain, scientists at McMaster University in Ontario, Canada, discovered that the part of the brain thought to be related to mathematical reasoning - the inferior parietal region - was 15 percent wider on both sides than normal.
Furthermore, they found that the groove that normally runs from the front of the brain to the back did not extend all the way in Einstein's case. That finding could have applications even to those with more pedestrian levels of intelligence.

Einstein thought in images
"That kind of shape was not observed in any one of our brains and is not depicted in any atlas of the human brain," said Sandra Witelson, a neuroscientist who led the study, published in this week's issue of The Lancet, a British medical journal.
"But it shouldn't be seen as anatomy is destiny," she added. "We also know that environment has a very important role to play in learning and brain development. But what this is telling us is that environment isn't the only factor."
The findings may point to the importance of the inferior parietal region, Witelson said.
While the differences may be extraordinary between Einstein and everyone else, there may be more subtle, even microscopic, differences when the anatomies of the brains of people who don't fall into the genius category are compared with each other, she said.
The researchers compared the founder of the theory of relativity's brain with the preserved brains of 35 men and 56 women known to have normal intelligence when they died.
With the men's brains, they conducted two separate comparisons - first between Einstein's brain and all the men, and next between his brain and those of the eight men who were similar in age to Einstein when they died.
They found that, overall, Einstein's brain was the same weight and had the same measurements from front to back as all the other men, which Witelson said confirms the belief of many scientists that focusing on overall brain size as an indicator of intelligence is not the way to go.
Witelson theorized that the partial absence of the groove in Einstein's brain may be the key, because it might have allowed more neurons in this area to establish connections between each other and work together more easily.
She said it is likely that the groove, known as the sulcus, was always absent in that part of Einstein's brain, rather than shrinking away as a result of his intelligence, because, as one of the two or three landmarks in the human brain, it appears very early in life.
"We don't know if every brilliant physicist and mathematician will have this same anatomy," Witelson said. "It fits and it makes a compelling story, but it requires further proof."
John Gabrieli, an associate professor of psychology at Stanford University who was not connected with the study, said the finding relating to the groove and connections between the neurons in the brain may be the key.
"We don't have a clue, so anything that is suggested is interesting," he said. "There must have been something about his brain that made him so brilliant."
Brilliance of the kind Einstein possessed is so extreme, however, that although the findings may give a clue to the neurology of genius, whether they could apply to normal differences in intelligence is more doubtful, Gabrieli said.
Witelson said the next stage is to scan the brains of living mathematicians and look for minute differences.
Witelson and her team acquired Einstein's brain after they were contacted by its keeper, scientist John Harvey, who had read about the university's brain research.
Harvey was a pathologist working at a small hospital in Princeton, N.J., when Einstein died in 1955 at the age of 76. Harvey performed the autopsy, determined Einstein died of natural causes and took the brain home with him.
Some parts of the brain were given to scientists, but no major study was ever conducted, until now.
The Einstein Cross Gravitational Lens - NASA
Albert Einstein - Wikipedia
Another Biography
Einstein Photos
NOVA Online
Einstein Archives Online
Einstein speaking about the Holocaust: (MP3 File)
Einstein's Theories on Science and Religion - 1941

Quote about Crustal Displacement
"In a polar region there is a continual deposition of ice, which is not symmetrically distributed about the pole. The earth's rotation acts on these unsymmetrically deposited masses [of ice], and produces centrifugal momentum that is transmitted to the rigid crust of the earth. The constantly increasing centrifugal momentum produced in this way will, when it has reached a certain point, produce a movement of the earth's crust over the rest of the earth's body, and this will displace the polar regions toward the equator. " From The Path of the Pole by Charles Hapgood.
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