The Parallel Axioms
Channel: Andrew Misseldine
Date: 2022-01-11

In this video, we discuss the three alternative parallel postulates that can be satisfied by an incidence geometry, namely the elliptic parallel postulate, the Euclidean parallel postulate, and the Hyperbolic parallel postulate. We introduce handshake geometry to provide an infinite family of finite hyperbolic geometries.

This is part 7 (2/4) of the lecture series offered by Dr. Andrew Misseldine for the course Math 3130 - Modern Geometries at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at: 
https://drive.google.com/file/d/1puToiyiACDz1J0wVxnbTjmyJv3o2gsqo/view

This lecture is loosely based upon Section 1.4 of Roads to Geometry by Wallace & West. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.