
Re: rational ngon inscribed in a unit circle
Posted:
Dec 12, 2013 6:12 PM


In article <v9eka95fgncieb1ad141kf29eual2o3abm@4ax.com>, quasi <quasi@null.set> wrote:
>Close, but I don't think the above example works for >radius 13.
That's floating point for you. Do you have a way to check analytically?
>Conjecture (1) [revised]: > >If n > 6, there does not exist a rational ngon with pairwise >distinct edge lengths and no two vertices diametrically >opposite which can be inscribed in a unit circle.
Possible solutions I have with no repeated edges are
radius 21, 9 sides: 1 2 5 10 11 12 17 30 34 radius 23, 8 sides: 1 8 13 16 18 20 29 32 radius 24, 7 sides: 1 10 13 15 16 38 42
but I suspect they are all near misses. I haven't checked for diametrically opposite vertices.
 Richard

