quasi
Posts:
10,188
Registered:
7/15/05


Re: rational ngon inscribed in a unit circle
Posted:
Dec 13, 2013 4:08 AM


Richard Tobin wrote: >quasi 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?
In principle, yes.
I'll play with it.
But numerically, it's clear that your example with 35 sides and radius 13 _almost_ works, but doesn't _actually_ work.
>>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.
Yep, they all miss by a little bit.
quasi

