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

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”

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

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"

“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"

“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.