Answer:
Proved
Step-by-step explanation:
Given
[tex]n = 6[/tex] --- sides of hexagon
[tex]l = 1[/tex] --- side length
Required
Prove that for 7 points picked from the interior, 2 points are at most 1 unit apart
1. Draw a hexagon (see attachment)
2. Divide the hexagon into 6 triangles
3. Select 7 points on the hexagon
You will notice that at least 2 points will be in one of the triangle.
The maximum distance between these two points is 1 unit. This is because
1. The triangle is equilateral (all sides equal)
2. The length of each is 1 unit (in other words, the distance between points, cannot exceed the side length)
