quasi
Posts:
12,023
Registered:
7/15/05


Re: rational ngon inscribed in a unit circle
Posted:
Dec 11, 2013 4:04 PM


fom wrote: >quasi wrote: >>scattered wrote: >>>quasi 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? >>> >>>Why not multiply your question by the LCM? When can ngons >>>whose sides are integers be inscibed inside of a circle of >>>integer radius? >> >>Yes, it's the same question. >> >>I just chose to state the question using radius 1 and rational >>edge lengths. > >If you state the question so that both the radius and the side >are even natural numbers, would this not reduce to a question >concerning Pythagorean triples?
At some level, surely.
But not in any immediate way.
To attack the problem, rescaling so that all rational lengths are integers is a fine first step, but no instantly apparent integral right triangles arise directly from such a rescaling.
quasi

