MATH 5200: Foundations of Geometry

Welcome to the homepage for Foundations of Geometry (Math 5200/7200)!

In Spring 2023, I’m substitute teaching this course for a short period. So this webpage contains only a few classes worth of material.

Office hours are in-person: 4-6pm on Wednesdays, in Boyd 448. Help is also available at the Math Department Study Hall, Monday-Thursday 3-7pm in McBay Science Library 382.

Course Material

1. (1/23) Video: A Tale of Two Matrices
   1. Active Learning: Exploring a point group
   2. Online resource: desmos matrix calculator
2. (1/25) Video: Of symmetries, solids and coordinates
   1. Active Learning. Orbits of the Delightful Dozen.
   2. Optional reading: Coxeter, Regular Polytopes, Chapter 3.
   3. Optional reading: Verheyen, The complete set of Jitterbug transformers and the analysis of their motion.
3. (1/27) Barycentric coordinates and the structure of a general orbit
   1. Active Learning: The General Orbit
4. (1/30) A three-dimensional map: building a tetrahedral map of the orbit
5. (2/1) Tensegrity Theory: The duality between stresses and rigidity
6. (2/3) Building a symmetric tensegrity