(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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].

2. Relevant equations

None.

3. 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Geometry (an interesting question with a hard proof)

**Physics Forums | Science Articles, Homework Help, Discussion**