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Topic: rational n-gon inscribed in a unit circle
Replies: 59   Last Post: Dec 19, 2013 12:56 AM

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 quasi Posts: 12,012 Registered: 7/15/05
Re: rational n-gon 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

>
>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 n-gon 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

Date Subject Author
12/10/13 quasi
12/10/13 ross.finlayson@gmail.com
12/10/13 quasi
12/11/13 quasi
12/11/13 quasi
12/11/13 quasi
12/12/13 quasi
12/12/13 Helmut Richter
12/12/13 quasi
12/11/13 scattered
12/11/13 quasi
12/11/13 fom
12/11/13 fom
12/11/13 quasi
12/11/13 fom
12/11/13 Richard Tobin
12/11/13 Richard Tobin
12/12/13 quasi
12/12/13 Richard Tobin
12/12/13 Richard Tobin
12/12/13 quasi
12/12/13 Brian Q. Hutchings
12/13/13 quasi
12/13/13 Brian Q. Hutchings
12/12/13 Thomas Nordhaus
12/12/13 Richard Tobin
12/12/13 quasi
12/12/13 Richard Tobin
12/12/13 quasi
12/12/13 quasi
12/13/13 Richard Tobin
12/13/13 Richard Tobin
12/13/13 quasi
12/13/13 Richard Tobin
12/13/13 quasi
12/13/13 Richard Tobin
12/13/13 quasi
12/13/13 quasi
12/12/13 Richard Tobin
12/13/13 quasi
12/13/13 Richard Tobin
12/13/13 quasi
12/14/13 quasi
12/14/13 quasi
12/14/13 quasi
12/14/13 quasi
12/14/13 Richard Tobin
12/15/13 quasi
12/15/13 quasi
12/15/13 Richard Tobin
12/15/13 David Bernier
12/15/13 quasi
12/18/13 Richard Tobin
12/18/13 ross.finlayson@gmail.com
12/19/13 quasi
12/14/13 Richard Tobin
12/14/13 quasi
12/14/13 Richard Tobin
12/14/13 ross.finlayson@gmail.com
12/15/13 Brian Q. Hutchings