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Nov 15, 2012 at 9:50 comment added Roland Bacher Sorry, since I can accept only one answer and since Joseph O'Rourke mention of the Erdos-Szekeres paper kills the problem completely, I have changed the accepted answer to his reply.
Nov 14, 2012 at 10:01 comment added Pietro Majer Yes, it seems a beautiful and difficult variational problem.
Nov 14, 2012 at 9:14 comment added Roland Bacher Indeed. So what is the best possible constant for a given integer $n$?
Nov 14, 2012 at 9:13 vote accept Roland Bacher
Nov 15, 2012 at 9:47
Nov 14, 2012 at 8:54 history answered Pietro Majer CC BY-SA 3.0