# Happy Ending Problem

- Author:
- John Golden

- Topic:
- Quadrilaterals

This sketch is inspired by a great story at Pat Bellew's math history blog.
The theorem (illustrated here for the smallest case) involves Esther Klein, Paul Erdos and George Szekeres, plus the birth of combinatorial geometry,
and the marriage of two mathematicians!
http://pballew.blogspot.com/2014/08/the-end-for-happy-ending-couple.html
This theorem is also covered at Theorem of the Day:
http://www.theoremoftheday.org/GeometryAndTrigonometry/EstherKlein/TotDEstherKlein.pdf
The question is: given 5 points in the plane, can you arrange them so any 4 of them form a concave quadrilateral?

More GeoGebra at bit.ly/mh-ggb