Reply
Fri 15 Apr, 2016 02:02 am

Squaring Numbers a New Way by PiyushGoel

If we talk about Square,Square is the result of multiplying a number by itself.From ancient lot creative man has given lot to Mathematics about Squaring and more yet to come into existence,one of Mathematics Lover PiyushGoel has done more in Squaring.

If we square 11,simply put 1(2*1)(1^2) get 121 same as square of 12 = 1(2*2)(2^2) get 144 and for 13&14 get receptively 169 196.

Look at (2,4,6,8,10,12 ,14,16,18,20 …diff of 2) & (1, 4 , 9 ,16,25,36,49,64,81,100 ……diff. is 3 5 7 9 11 13 15 17 19) and diff. of 3 5 7 9 11 is 2, so there is true symmetry of 2.

11^2 = 1 2 1

12^2 = 1 4 4

13^2 = 1 6 9

14^2 = 1 8 16 = 100 + 80 + 16 = 196

15^2 = 1 10 25 = 100 + 100 + 25 = 225

16^2 = 1 12 36 = 100 + 120 + 36 = 256

17^2 = 1 14 49 = 100 + 140 + 49 = 289

18^2 = 1 16 64 = 100 + 160 + 64 = 324

19^2 = 1 18 81 = 100 + 180 + 81 = 361

20^2 = 1 10^2 = 1 20 100 = 100 + 200 + 100 = 400

21^2 = 1 11^2 = 1 22 121 = 100 + 220 + 121 = 441

22^2 = 1 12^2= 1 24 144 = 100 + 240 + 144 = 484

23^2 = 1 13^2 = 1 26 169 = 100 + 260 + 169 = 529

24^2 = 1 14^2 = 1 28 196 = 100 + 280 + 196 = 576

25^2 = 1 15^2 = 1 30 225 = 100 + 300 + 225 = 625

26^2 = 1 16^2 = 1 32 256 = 100 + 320 + 256 = 676

27^2 = 1 17^2 = 1 34 289 = 100 + 34 + 289 = 729

28^2 = 1 18^2 = 1 36 324 = 100 + 360 + 324 = 784

29^2 = 1 19^2 = 1 38 361 = 100 + 380 + 361 = 841

30^2 = 1 20^2 = 1 40 400 = 100 + 400 + 400 = 900

31^2 = 1 21^2 = 1 42 (1 11)^2 = 1 42 (1 22 121)

= 961 = 121 + 220 + 100

= 441 + 420 + 100 = 961

41^2 = 1 31^2 = 1 62 (1 21)^2 = 162 (1 42) (1 11)^2

= 1 62 (1 42) (1 22 121)

= 1 62 (961) = 961 + 620 + 100 = 168

Copyrighted to PiyushGoel

@PiyushGoel,

Forget the copyright rubbish !

Learn a bit of elementary algebra to understand that your 'method' is a convoluted restatement of the identity

(a+b)^2 = a^2+2ab+b^2

e.g.

41^2 = (40+1)^2 = 40^2 + 2*40*1 + 1^2 =1600 + 80 + 1 = 1681

alternatively, you can make it

*more* complicated LIKE YOU by writng

41 as a different combination, such as 30+11 etc !

@PiyushGoel,

...or 10+31, giving 10^2+2*10*31+31^2=100+620+900+60+1

....YOUR GROUPING !