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.
The Klein Bottle and Projective Plane - Algebraic Topology - NJ Wildberger
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Overview
Syllabus
Introduction
Loop of lines
Klein bottle
Projective plane
Introducing a sphere
Introducing a disc
Making it square
Glue it together
Taught by
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