Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the th polygon is the circumcircle
of the st
and successive polygons are rotated one half-turn at each iteration. The results
are shown above for nested triangles through heptagons in alternating black and white
and in a cyclic rainbow coloring.

The animation above shows successive iterations of a nested octagon.

Gardner, M. The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University
of Chicago Press, pp. 165-166, 1984.Kabai, S. Mathematical Graphics
I: Lessons in Computer Graphics Using Mathematica. Püspökladány,
Hungary: Uniconstant, p. 97, 2002.