I teach geometry, so I get asked this question a lot.

Of course, the subject has many uses, from architecture to the study of ziggurats, but I don’t like to focus on tawdry, real-world uses for it. Geometry is far too important to me for its value to be measured in terms of mere utility.

Without the octadecagon and the nonagon, and my curiosity about them, for example, I never would have come up with this pattern:

Was it useful for me to do this? Such a question would miss the point completely. It was FUN to make this, and that’s why I did it. While I worked on it, I thought about absolutely nothing that bothers me. The rest of the world vanished, leaving only a mathematical pattern, and I was completely happy.

I guess one could look at this as a “use,” but — yuck — I certainly do not want to.