The Chromatic Number of the Plane
I made a discovery relating to this topic -- a
new coloring of the plane in seven colors.
What is the minimum number of colors needed to color the plane so that
no two points of the same color are exact one unit apart? If you
look at the figure above, you can see that the answer is at most seven
colors. A few unit circles have been included on the diagram.
If you look at the widget below, you'll see that answer is four colors
or more. Just toss it onto the plane. It's not hard to prove
that at least four colors are necessary.