Note, too, that there are lines of symmetry (4 diameters). . .
. . . and a rotation of 8 sectors cut by them at equal angle intervals at the center.
These and other relationships are perceived in an ordinal way. Sets of concentric and parallel line segments accumulate in dramatic complexity as the grid grows and becomes more elaborate.
This approach to learning about geometry is motivating and non-threatening. It is very like making mandalas, which Dr. Carl Jung believed had powers to soothe the soul.
The circle is a finite field. The inscribed octagon has a seemingly infinite potential for combinations of line segments and 'hidden' (ambivalent) shapes. Every regular polygon can be inscribed.
The circle is itself the envelope of possibilities. Every regular polygon has its own unique grid and kaleidoscopic possibilities. Exploring these permutations and combinations opens a wide aperture into a world of awesome complexity, beauty, and ORDER.
Home || The Math Library || Quick Reference || Search || Help