Given 5 coplanar points with no three collinear, prove that there must be a subset of 4 points that form a convex quadrilateral.

(In reply to another proof by Charlie)

In you final case:

If the two outer points are within the same vertical angle, then the line connecting these two points will separate the triangle into two parts, with two points on one side and one point on the other.  The two points that are on one side, together with the two outer points, then form a convex quadrilateral.

However the line is not guaranteed to split the triangle.  This is easily fixed with an extra sub-case.

Posted by Jer on 2009-10-06 17:52:27