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 subcase.

Posted by Jer
on 20091006 17:52:27 