Math 618

(Last Updated January 6, 2022 @ 12pm)

Materials

A gamification of Euclidean geometry. It is a lot of fun and quite challenging. It is a nice introduciton to some of the Euclidean geometry we will discuss in the first part of the semester. It also serves as a nice visualization for proofs via construction, which is how the Greeks thought of much of mathematics.

Week 1 (1/31--2/4)

As briefly mentioned in class, Euclid's axioms are incomplete. In 1899, Hilbert wrote a book giving a more rigorous and complete axiomatic approach to geometry. Hilbert requires 20 axioms in his approach. Read more on Wikipedia: https://en.wikipedia.org/wiki/Hilbert's_axioms.

Videos

These videos should be watched after class Wednesday, February 2 and before class on Monday, February 7.

Introduce the notion of congruence and two congruence theorems (side-angle-side and side-side-side).Introduct the notion of parallelism and establish the Euclidean theorems about parallel lines that hold for all absolute geometries.