Pascal’s triangle“shape”is the essence of the counting arts 幂型为算法之源

Pascal’s triangle“shape”is the essence of the counting arts

the middle keep adding number is odd number keep going.

Plus the middle keep adding number I could get the number itself multiply itself

1²=1  

2²=4    1+3=4

3²=9    1+3+5=9

4²=16   1+3+5+7=16

5²=25   1+3+5+7+9=25

6²=36   1+3+5+7+9+11=36

7²=49   1+3+5+7+9+11+13=49

8²=64   1+3+5+7+9+11+13+15=64

9²=81   1+3+5+7+9+11+13+15+17=81

10²=100 1+3+5+7+9+11+13+15+17+19=100

Since it has law of Addition and multiplication, then law of subtraction division would naturally in it :

10²=100   100-19 (that the middle keep adding number)=81

9²=81    81-17 (that the middle keep adding number) =64

8²=64    64-15=49

7²=49    49-13=36

6²=36    36-11=25

5²=25    25-9=16

4²=16    16-7=9

3²=9     9-5=4

2²=4     4-3=1

The left :one (一)，two（二）， three（三） …… is original number.

The middle is the keep adding number added by original numbers keep adding   like 1+2=3   ；3+2=5  ………

Until 8+9=17. ……

The right is the original number itself multiply itself.

The number itself multiply itself is done by the keep adding number’s sum. From it I could get the law of Addition and multiplication. Oh, Then the law of subtraction and division in it also. Since then ,it would multiply till ∞.

Now I observe the tortoise matrix .I got square root; I got the law of Addition ;subtraction; multiplication; division, and Pythagoras theorem. It’s the tortoise matrix have not action yet already have those laws silently…….