The Klein Bottle and Projective Plane - Algebraic Topology - NJ Wildberger

Explore the Klein bottle and projective plane in this eighth lecture of a beginner's course on Algebraic Topology. Investigate the five Platonic solids and learn about Euler's formula relating vertices, edges, and faces. Follow a proof using triangulation and flow down a sphere. Delve into topics such as loops of lines, introducing spheres and discs, and the process of gluing shapes together to form complex topological structures.

Introduction
Loop of lines
Klein bottle
Projective plane
Introducing a sphere
Introducing a disc
Making it square
Glue it together