Hadwiger-Nelson problem


Definition

How many colors are needed to color the plane so that no two points at unit distance are the same color?
THEOREM    The number of colors needed to color the plane, so that no two points at unit distance are the same color, is greater than three, and less than or equal seven.

Proof available

THEOREM    The centroid divides each median into segments with a 2:1 ratio.

Proof available