This algorithm also applies to triangles, pentagons, 17-gons, and 65537-gons (all fermat prime polygons)!
You may have known the steps to construct a 257-gon from my previous videos, but I never told you why 257-gons are constructed like they are. I tried to simplify the math as much as possible: The most advanced concept in this video is the sigma notation.
Correction at 6:33. Other prime numbers can also have numbers which generates all the integers. I didn't realize that 129 wasn't prime, which is why it didn't work for 129. The real reason why only Fermat primes work is probably due to it being 1 more than a power of 2, and the method to find a point involves dividing by 2 repeatedly until you reach 1, which is only possible if the number points to divide is a power of 2.
A huge thanks to:
https://kenbrakke.com/RulerAndCompass/big-gon.html
https://www.researchgate.net/publication/225263489_The_Simple_and_straightforward_construction_of_the_regular_257-gon
Timestamps:
0:00 Intro
0:26 Fermat Primes
01:36 Nth Roots of Unity
03:46 Finding the X Position of a Point
15:28 Constructing the Polygon