Constructibility of Regular Polygons

This lecture covers the constructibility of regular polygons with a focus on the Gauss-Wantzel theorem, which states the conditions for a regular polygon to be constructible with a compass and straightedge. It also explores Fermat numbers, their properties, and their role in determining the constructibility of polygons. The lecture delves into the history of the conjectures of Fermat and their verification, highlighting the significance of Andrew Wiles' proof in 1995. Additionally, it discusses the fundamental role of the compass in geometric constructions, showcasing the works of Georg Mohr and Lorenzo Mascheroni.