Squares and Pigeonhole Principle
Let S be a square region of side length 2. Show that among any 9 points in the square, there are 3 which form a triangle of area .
I subdivided S into 8 triangles of equal area, .
Now I divide into 2 cases
Case A: Where 3 points are in one triangle.
Then the area of said triangle .
Case B: A max of 2 points are in any triangle
I'm having trouble with this case. Help please?
Re: Squares and Pigeonhole Principle
Consider a unit square, a square of side length one and area of one square unit.
Originally Posted by I-Think
Any three points from that unit square that do form a triangle,
The area of such a triangle is square units.
Can you show that?
Now divide your given square into four sub-squares each of one square unit each.
Can you finish?