The Arithmetic Sequence of the tortoise （等差数列）

The Arithmetic Sequence of the tortoise 

  Horizontal     4+9+2=15              3+5+7=15            8+1+6=15  

  Vertical         4+3+8=15              9+5+1=15            2+7+6=15    

 Diagonal line   4+5+6=15             2+5+8=15

The “center 5” ×3 = 15

If view the “tortoise” matrix is ordinal numbers

1      2     3     4     5     6      7      8       9     10

1^st  2^nd   3^rd   4^th  5^th   6^th   7^th   8^th   9^th    10^th

 

Horizontal    4th+9th+2nd=15th     3rd+5th+7th=15th      8th+1st+6th=15th   

Vertical      4th+3rd+8th=15th          9th+5th+1st=15th    2nd+7th+6th=15th     

Diagonal line   4th+5th+6th=15th       2nd+5th+8th=15th

The “center 5th” ×3=15th

I randomly give the Arithmetic Sequence 0.4. Don't have to be 0.4. As long as it is the Arithmetic Sequence，that will do.

0.4    0.8   1.2    1.6    2     2.4    2.8   3.2    3.6    4

1^st   2^nd   3^rd    4^th   5^th   6^th      7^th  8^th    9^th   10^th

Horizontal    4th+9th+2nd      3rd+5th+7th     8th+1st+6th

               1.6+3.6+0.8=6   1.2+2+2.8=6     3.2+0.4+2.4=6

Vertical      4th+3rd+8th      9th+5th+1st=15    2nd+7th+6th=15

              1.6+1.2+3.2=6    3.6+2+0.4=6      0.8+2.8+2.4=6 

Diagonal line   4th+5th+6th     2nd+5th+8th

                1.6+2+2.4=6     0.8+2+3.2=6

The “center 5th” that it is 2 here ×3=6

Their Horizontal line; Vertical line; Diagonal line and their “center 5th”×3 all equal 6.

This Arithmetic Sequence is one：

If I don't give the Arithmetic Sequence 0.4, I give the Arithmetic Sequence 1.3

1.3    2.6    3.9   5.2    6.5    7.8    9.1   10.4    11.7    13

1^st  2^nd   3^rd  4^th  5^th   6^th  7^th  8^th    9^th   10^th

                                          ^↓

Horizontal    4th+9th+2nd           3rd+5th+7th         8th+1st+6th

               5.2+11.7+2.6=19.5   3.9+6.5+9.1=19.5   10.4+1.3+7.8=19.5

Vertical      4th+3rd+8th       9th+5th+1st=15     2nd+7th+6th=15

             5.2+3.9+10.4=19.5   11.7+6.5+1.3=19.5     2.6+9.1+7.8=19.5

Diagonal line   4th+5th+6th          2nd+5th+8th

                5.2+6.5+7.8=19.5    2.6+6.5+10.4=19.5

The “center 5th” that it is 6.5 here ×3=19.5

Their Horizontal line; Vertical line; Diagonal line and their “center 5th”×3 all equal 19.5.

Play it fancier 

               ↓

I randomly give the Arithmetic Sequence 0.4. Don't have to be 0.4. As long as it is the Arithmetic Sequence，that will do.

4+3+5+7+6  that：

4^th+3rd+5^th+7^th+6^th

^{1.6+1.2+2+2.8+2.4=10}

2+9+5+1+8 that

2nd+9^th+5^th+1st+8^th

0.8+3.6+2+0.4+3.2 = 10

( comments: the horse matrix also could be played with Arithmetic Sequence like that and appear the law and the “character” of the horse matrix.)