
Re: rational ngon inscribed in a unit circle
Posted:
Dec 11, 2013 5:18 PM


In article <tlcfa9p32813b7jn9ho5j0q5j9b03htgpb@4ax.com>, quasi <quasi@null.set> wrote: >Call an ngon rational if all edge lengths are rational. > >For n > 6, does there exist a rational ngon which can be >inscribed in a unit circle?
If you could find an angle 0 < a < 60 such that sin(a) and sin(60a) are both rational, you could add some sides to a regular hexagon.
The case for sin(a) and sin(90a) (= cos(a)) rational is wellknown  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.
 Richard

