What is an enneagram?

You mean this?

http://en.wikipedia.org/wiki/Enneagram_of_Personality

My college classmate, Judith R. Searle wrote the definitive book and gives workshops.

Google

I’m looking for the mathematical meaning. When you divide (1/7, 2/7, 3/7, 4/7, 5/7, 6/7, 7/7, 8/7, 9/7), the number string 1,4,2,8,5,7 repeats in the decimals. Take the circle of the enneagram, 9 on the top, then 1 though eight clockwise, connect the string 1, 4,2,8,5,7, and you get the enneagram. So there has to be something other than personality as the meaning.

Mathematics is not really about “meaning”. There’s all kinds of interesting connections between numbers in mathematics (pi is a very common one, phi and e both come up all over the place). http://www.amazon.com/s/ref=nb_ss_gw/102–8150748-4111320?url=search-alias%3Daps&field-keywords=golden+ratio&x=0&y=0

Noticing that the sequence of connections of the enneagram—I would guess that since you’re constructing it with three equilateral triangles, and so that you’re skipping every other point (1 -> 4 skips 2 and 3) means that you’re probably doing something with the number 7, e.g., 9 – 2 = 7. But I’m pretty sure it has no (real) basis in geometry.