Squaring Numbers a New Way ............

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