Geometry and Groups #3 - Duality - LearnMathsFree





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Published on Aug 29, 2015

In this video, we introduce the definition of duality and how to construct the dual P* of a Platonic solid P. In the next video, we'll look at group actions with the aim of classifying the symmetry groups of the Platonic solids.

"Dual Cube-Octahedron" by 4C. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/Fi...

This is a course that loosely follows the syllabus of UCL's course on the subject, that seeks to explore the fascinating links between group theory and geometry, starting with the Platonic solids and hopefully culminating in a discussion of the modular group, PSL(2,Z). More specifically, in this playlist I'd like to explore:

-Symmetry groups of Platonic solids
-Spherical and hyperbolic geometry
-A complete classification of Mobius transformations
-Isometries of hyperbolic space
-Euclidean space and quaternions

*Taught in 2014-2015.

Video URL: https://youtu.be/-xzWyb6AW7s
Channel URL: https://www.youtube.com/channel/UCtTF...

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