Wednesday, June 13, 2007

The Happy Ending problem

The Happy Ending problem (so named by Paul Erdős since it led to the marriage of George Szekeres and Esther Klein) is the following statement:

Theorem. Any set of five points in the plane in general position(no two points coincide and no
three points are collinear) has a subset of four points that form the vertices of a convex quadrilateral.

Quite misleading!

2 comments:

gregarious dude said...
This comment has been removed by the author.
gregarious dude said...

Hi. It's actually quite simple visually if you just construct a triangle with two points inside. You should read the article on www.mathworld.com, if you haven't already. It's easy to understand at least.