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The Earth-Moon Problem
A Notorious and Surprisingly Simple Unsolved Math Problem
I’ve become a bit obsessed lately with reading about unsolved problems in graph theory. Graph theory is such a fun and visual field of mathematics that is absolutely bursting with open problems. Even better, these problems usually aren’t too difficult to understand. That includes the main topic of this article: the Earth-Moon problem.
Before I can go into the Earth-Moon problem, we have to cover some of the basics of graph theory. It’s not the typical graph with x and y axes. A graph is a mathematical object composed of nodes (the dots) and edges (the lines connecting them). Below, I have an example of a simple graph where each node is labeled with a number. Not all graphs have their nodes labeled this way.
We can extend the concept of a graph with all sorts of different ideas. One of the most common ways to study graphs is by coloring the nodes. It’s often important to distinguish how many different colors are being used to color the nodes in a given graph. For example, the graph below has had its nodes colored with red, green, and blue. Notably, it has been done so in a way that no colored…
