Nine Point Circle

Let us try to find the digit sum of numbers starting from 1, 2, 3, 4, and so on.

Number:    1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 . . . 51, 52, 53, . . .

Digit Sum: 1, 2, 3, 4, 5, 6, 7, 8, 9, 1,    2,    3,  4,    5,   6,    7,   8,   9,   1,    2,  3,         6,   7,   8, . . .

If you see the above Digit Sums, then a new pattern is created. The digit sums keep cycling from 1 to 9. And when we plot this, then a circle of 9 is formed.

Also, if we add 9 or a multiple of 9 to any number, it is the same as adding 0 in digit sum.

For example:

Digit Sum of 17 is 1+7 = 8

Now, Digit Sum of 26 (17+9) is 2+6 = 8.

Effectively, 0 and 9 are same in Digit Sums.