Can you draw Regular Shapes perfectly on a Grid?

Patreon:   / polyamath   Instagram:   / polya.math   Discord:   / discord   We explore which regular polygons (that is, shapes with equal-length sides and equal interior angles) can be drawn on a grid with their vertices at integer coordinates. In the end, we cover 4 different arguments (some more detailed than others) and finish off with one of my favourite visual proofs! Software: (entirely) DaVinci Resolve GitHub: https://github.com/NishadDeulkar/Poly... Source for the solution at the end: https://jdh.hamkins.org/no-regular-po... (I found all the other solutions myself) ___________________________________________________________________________________________________ Chapters: 0:00 The Problem 0:50 Equilateral Triangles 4:43 All Regular Polygons 12:53 More (Very Pretty) Proofs!! ___________________________________________________________________________________________________ Music: It's Raining Somewhere Else - Toby Fox (Undertale) Undercover Vampire Policeman - Chris Zabriskie Dancing Star - Aakash Gandhi Waterfall - Aakash Gandhi