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!

4 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.

kold_kadavr_ flatliner said...

Let this be your catalyst to Seventh-Heaven:

'The more you shall honor Me,
the more I shall bless you'
-the Infant Jesus of Prague
(<- Czech Republic, next to Russia)

Love him or leave him or indifferent...
better lissen to the Don:

If you deny o'er-the-Hillary's evil,
which most whorizontal demokrakkrs do,
you cannot deny Hellfire
which YOU send YOURSELF to.

Yes, earthling, I was an NDE:
the sights were beyond extreme.
Choose Jesus.
You'll be most happy you did.
God bless your indelible soul.

kold_kadavr_ flatliner said...

Let this be your catalyst to Seventh-Heaven:

'The more you shall honor Me,
the more I shall bless you'
-the Infant Jesus of Prague
(<- Czech Republic, next to Russia)

Love him or leave him or indifferent...
better lissen to the Don:

If you deny o'er-the-Hillary's evil,
which most whorizontal demokrakkrs do,
you cannot deny Hellfire
which YOU send YOURSELF to.

Yes, earthling, I was an NDE:
the sights were beyond extreme.
Choose Jesus.
You'll be most happy you did.
God bless your indelible soul.