How to Construct a 257-gon

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 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. However, 33, 65, 129, 513, 1025, 2047 and other powers of 2 plus 1 are not prime, and only numbers in the form of 2^2^n + 1 are prime. 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