There are [itex]n > 3[/itex] points in the plane such that any three of the points form a triangle of area [tex] \leq 1[/tex]. Show that all n points lie in a triangle of area [tex]\leq 4[/tex].
The Attempt at a Solution
This is hard to discribe since it is immposible to "draw" on a computer.
However, I think this problem may not have been stated correctly, becuase, if we choose our 3 points to be the vertices of a triangle with area = 4, then we found a contradiction.
Although, if I am wrong and this problem is correct, i thought that proving the contrapostivie proves the question.
Can somebody please help me out?