Digital Root: A Strangely Interesting Operation

[willr12]

Digital root (adding a number's digits together repeatedly until a single digit answer is obtained) doesn't seem like a very interesting operation, but it has some weird properties. One of the first someone might notice is that
dr(n) = dr(n+9)
This is fairly easy to demonstrate. But after graphing the digital roots of the first 9 multiples of n with values of 9 from 1-9, a seemingly uninteresting operation looks pretty cool. Notice how dr(n) always goes through (9/2, 9/2)
Doesn't really have any implications towards anything but looks pretty cool.

 

[mathman]

This technique can be used to determine if a large number is a multiple of 9 - with single digit of 9, or a multiple of 3 - single digit 3, 6, or 9.

 

[willr12]

This technique can be used to determine if a large number is a multiple of 9 - with single digit of 9, or a multiple of 3 - single digit 3, 6, or 9.

Each number has a digital root pattern, that's for 3. For example, 4 is 4,8,3,7,2,6,1,5,9