Galois theory: Heptadecagon

This lecture is part of an online graduate course on Galois theory.

As an application of Galois theory, we prove Gauss's theorem that it is possible to construct a regular heptadecagon with ruler and compass.

[rainerausdemspring]

A friend from Italy has confirmed that 17 is a bad luck number in Italy.

[hugolabella]

Imagine actually constructing that 65537 polygon with ruler and compass.

[caspermadlener]

I actually proved that you can do the same constructions with only a compass.
The proof requires a really interesting step! Proving that every algebraic number is bounded!

[tim-cca]

14:52 p is prime so n=2^k, and it is Fermat prime

[Suav]

10:14 that's a lecture and a seminar jumped over in 5 seconds. So, if you happen to read this comment and you felt a bit lost a times - fill the gaps. In other words, this is a magnificent sketch of a route, but one has to do ones looking around on ones own.

[PopeLando]

It turns out that the Monster Group is the group of symmetries of the constructible polygon of the next Fermat Prime after 65, 537.

[migarsormrapophis]

ye



yeee yee yeee yee ye you 'The Flagged Dragon'

[paul]

Dear prof. Borcherds,

With due respect I am critical of your video's on mathematics. In all of your video's you display your vast knowledge of math but you do not give any proofs. They simply say: "I know all of this and if you do not I am sorry." What good are these video's doing other than that they will make people with the same level of knowledge happy?