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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: 11,740 Registered: 7/15/05
Re: rational n-gon inscribed in a unit circle
Posted: Dec 12, 2013 5:38 PM

Richard Tobin wrote:
>quasi wrote:
>

>>> n=8: 1/4 1/4 1/4 1 1 1 5/4 5/4
>
>>An 8-gon with those sides can't be inscribed in a unit circle.
>

When I replied, your correction wasn't yet visible on my
news server.

But yes, your corrected version works.

Very nice.

>I divided 9 by 8 and got 5/4.

Hehe.

>Here's a cyclic 35-gon with radius 13, maybe:
>
> 1 1 1 1 1 1 1 1 1 1
> 1 1 1 1 1 1 1 1 1 1
> 2 2 2 2
> 3 3 3 3 3 3 3 3
> 5 6 17

Close, but I don't think the above example works for

But nice work dispatching conjecture (1).

I'll try a revision ...

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.

Remark:

I think I've made it harder to beat, but I suspect it will
still fail. In any case, it makes for a nice challenge.

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