Existence of Rectangles
Channel: Andrew Misseldine
Date: 2020-03-19

In this video, we discuss the nature of rectangles and the related notion of the sum of angle measures of a triangle in neutral geometry, leading to the proof of the "All-or-Nothing" Theorem, which states that either all triangles have an angle measure sum of 180 degrees or none of them do. Both of these notions are equivalent to the Euclidean parallel postulate in neutral geometry.

This is part 26 (1/1) 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/1sLJ5U2BkwzPI-pVKPnBMRxhc-glyXPxt/view

This lecture is loosely based upon Section 3.6 of Euclidean and Non-Euclidean Geometries by Greenberg. 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.