In article <firstname.lastname@example.org>, quasi <email@example.com> wrote: >Call an n-gon rational if all edge lengths are rational. > >For n > 6, does there exist a rational n-gon which can be >inscribed in a unit circle?
If you could find an angle 0 < a < 60 such that sin(a) and sin(60-a) are both rational, you could add some sides to a regular hexagon.
The case for sin(a) and sin(90-a) (= cos(a)) rational is well-known - they are the angles of a pythagorean triangle - but that doesn't help much.
Google finds plenty on cyclic polygons with rational sides and area, but again I don't see how that helps.