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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: 10,451
Registered: 7/15/05
Re: rational n-gon inscribed in a unit circle
Posted: Dec 12, 2013 5:38 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.
>
>Correction already posted.


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
radius 13.

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
Read rational n-gon inscribed in a unit circle
quasi
12/10/13
Read Re: rational n-gon inscribed in a unit circle
ross.finlayson@gmail.com
12/10/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/11/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/11/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/11/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/12/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/12/13
Read Re: rational n-gon inscribed in a unit circle
Helmut Richter
12/12/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/11/13
Read Re: rational n-gon inscribed in a unit circle
scattered
12/11/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/11/13
Read Re: rational n-gon inscribed in a unit circle
fom
12/11/13
Read Re: rational n-gon inscribed in a unit circle
fom
12/11/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/11/13
Read Re: rational n-gon inscribed in a unit circle
fom
12/11/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/11/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/12/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/12/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/12/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/12/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/12/13
Read Re: rational n-gon inscribed in a unit circle
Brian Q. Hutchings
12/13/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/13/13
Read Re: rational n-gon inscribed in a unit circle
Brian Q. Hutchings
12/12/13
Read Re: rational n-gon inscribed in a unit circle
Thomas Nordhaus
12/12/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/12/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/12/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/12/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/12/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/13/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/13/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/13/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/13/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/13/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/13/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/13/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/13/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/12/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/13/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/13/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/13/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/14/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/14/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/14/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/14/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/14/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/15/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/15/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/15/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/15/13
Read Re: rational n-gon inscribed in a unit circle
David Bernier
12/15/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/18/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/18/13
Read Re: rational n-gon inscribed in a unit circle
ross.finlayson@gmail.com
12/19/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/14/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/14/13
Read Re: rational n-gon inscribed in a unit circle
quasi
12/14/13
Read Re: rational n-gon inscribed in a unit circle
Richard Tobin
12/14/13
Read Re: rational n-gon inscribed in a unit circle
ross.finlayson@gmail.com
12/15/13
Read Re: rational n-gon inscribed in a unit circle
Brian Q. Hutchings

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