Thursday, March 20, 2008

So, about the title...

A heptadecagon is a 17-sided polygon. Back in 1796, Gauss gave a proof of the constructibility by straight-edge and compass of a regular (all sides equal, all internal angles equal) heptadecagon. He liked the proof so much that he asked to have one carved onto his tombstone. According to the story, the engraver, telling Gauss that a heptadecagon carved on a stone would be essentially indistinguishable from a circle, declined.

196 years later, I took a class in Galois theory. Each of the five or six students in the class had to prepare a lecture on some mathematical topic relevant to the course material. My lecture consisted of working through Gauss's proof. I had always been a fan of geometry, but upon discovering the connections from straight-edge and compass constructions to algebraic equations, cyclotomic polynomials, and nth roots of unity, I felt as if I had just learned to do magic.

At this point, those few readers who don't find me exceedingly tedious may wish to ask me the question, "So, when you die, are you going to have a heptadecagon on your tombstone?" For this curious group, I offer my answer: Nope. There will be no heptadecagon. There won't even be a tombstone; I'm donating my body to science.