quasi
Posts:
10,660
Registered:
7/15/05


Re: rational ngon inscribed in a unit circle
Posted:
Dec 12, 2013 4:55 PM


Richard Tobin wrote:
>And is > > n=3: 200/145 232/145 288/145 > >a rational triangle not using a diameter?
Yes.
There are lots of rational nonright triangles which can be inscribed in a unit circle.
In one of my previous replies, I outlined a procedure which can be used to generate all such triangles.
Of the 4 conjectures I posed in this thread, all referred to rational ngons inscribed in a unit circle with n > 3.
Some status ...
I have counterexamples for conjectures (2),(3), and (4) including the first revision of conjecture (4).
As of now, conjecture (1) (the case n > 6) is still alive, but I don't expect it to survive.
Conjecture (4) (the case n = 4) has been reincarnated in a new revision (revision 2), and has survived some light testing.
Those are the only ones still open.
quasi

