This excellent question was posed at Challenging the enneagram

One is tempted to answer "because of the number line, duh!" or "that's just the way it is."

However, as with anything else, the answer isn't that simple, especially when represented by a diagram such as this:

It will be necessary to expand the picture in order to discern all of the numbers.

It's also necessary to know about the Laws of Three and Seven. Mathematically, these are expressed as:

1/3 = .333333...

2/3 = .666666...

3/3 = .999999...

1/7 = .1428571...

2/7 = .2857142...

3/7 = .4285714...

4/7 = .5714285...

5/7 = .7142857...

6/7 = .8571428...

Ignore the musical notes and their corresponding HZs on the chart (which correspond to the 7 major white keys on the keyboard, A - G), and consider purely the mathematics of this. Starting at point 9, at the top of the enneagram , you will see a .999999. At point 1 you will see .1428571..., At point 2 you will see .2857142..., At point 3 you will see .333333..., At point 4, .4285714..., point 5, .5714285..., point 6, .666666..., point 7, .7142857..., and point 8, .8571428...

Returning to the first yellow 9 on the inside of the colored circle, the numbers regress consecutively and clockwise from 9 to 1, creating 9 radials emanating from the center of the circle and intersecting the edge of the colored circle between each enneagram point (although imaginatively, they proceed beyond the edge). The first (1) just happens to land on point 1 on the enneagram. As the numbers regress around the circle, wrapping from 1 back to 9 again, each enneagram point just happens to correspond to points on the 9 - 1 clockwise regression.

Outside of the colored circle there are two concentric yellow circles with numbers lined up with the numbers on the inside of the circle. The two numbers on the imaginary line emanating from the edge of the colored circle, added up with the number inside the circle, numerologically must always add up to 3, 6, or 9. Starting with the yellow, vertical 999 at the top of the enneagram, 9+9+9 = 27, and 2+7 = 9. To the right of that you will see a 258. 2+5+8 = 15, and 1+5 = 6. To the right of that you will see a 417. 4+1+7 = 12, and 1+2 = 3. Etc.

The outside yellow circle, considered in clockwise fashion, contains consecutive odd and even numbers laid along in this pattern after the top number 9: 2, 4, 6, 8, 1, 3, 5, 7, 9, etc.

Adding up any 3 consecutive numbers on the inside yellow circle will always yield, numerologically, a 3, 6, or 9.

The colors of the numbers do have meaning, but as far as I can tell this is only to indicate correspondences with the Laws of 3 and 7. 3s, 6s, and 9s are always represented with yellow. 5s, 8s, and 2s, are represented with green, and 4s, 1s, and 7s are represented with red. Notice that they also hint at the points of integration and disintegration for points 1 and 8. Red and Green are also represented on the divisions by 7 on the inside of the circle. For example, .857142

And that's why point 7 lies between points 6 and 8 on the enneagram.