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Topic: regular n-gon runners problem
Replies: 12   Last Post: Jul 25, 2013 4:26 AM

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Registered: 7/15/05
Re: regular n-gon runners problem
Posted: Jul 23, 2013 4:28 AM
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William Elliot wrote:
>quasi wrote:
>> Suppose n runners, n >= 3, start at the same time and
>> place on a circular track, and proceed to run
>> counterclockwise along the track (forever), each at a
>> distinct positive constant speed.
>> Conjecture:
>> If there is an instant where the locations of the n runners
>> are the vertices of a regular n-gon, then the speeds of the
>> runners, arranged in ascending order, form an arithmetic
>> sequence.

>r1 <= r2 <=..<= r_n

The speeds were specified as distinct, so the inequalities are

>For j = 1,.. n, dj = rj.t, t = dj/rj, dj = j.d1
>rj/dj = r1/d1; rj = r1.dj/d1 = j.r1

I have no idea what you are trying to say above.


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