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

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 quasi Posts: 12,067 Registered: 7/15/05
regular n-gon runners problem
Posted: Jul 23, 2013 2:33 AM

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.

Remark:

It's easy to see that the converse holds.

quasi

Date Subject Author
7/23/13 quasi
7/23/13 Virgil
7/23/13 quasi
7/23/13 quasi
7/23/13 quasi
7/23/13 quasi
7/25/13 quasi
7/23/13 William Elliot
7/23/13 quasi
7/23/13 William Elliot
7/23/13 quasi
7/23/13 James Waldby
7/23/13 quasi