Math 618


(Last updated Friday, Feb. 26 at 2pm)

Meetings

The first class meeting will be on Monday, February 1 at 4:40pm.

After the first week of class, we will use Monday's class time as an office hour meeting 4:40p–5:40pm and we will have a live class session on Wednesdays 4:40–5:40pm.

All meetings will occur on Zoom (Zoom Link).

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 5 (3/1--3/5)

Introduce translations and basic properties. Proved that every translation is the composition of two reflections about parallel lines. Introduced reflections.

Week 4 (2/22--2/26)

We show that rigid motions preserve lines and are completely determined by their behavior on any one triangle.Introduce reflections and prove that they are rigid motions. We proved that every Euclidean rigid motion is the composition of at most three reflections.

Week 3 (2/15--2/19)

  • Schedule Change Notice: The college is closed on Monday in observance of President's day. Office hours on Monday are cancelled, but Wednesday's class time will be treated as an office hour. There is only one video for this week, since we would have lost a day during a regular in-person class.

  • Video 1 (Notes) --- Watch by end of the week

Introduced the notion of rigid motions.

Week 2 (2/8--2/12)

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. We proved that parallel lines exist in every absolute geometry. We then proved the first of Euclid's theorem's requiring his 5th postulate; we then discussed Playfair's postulated and proved that the sum of the angles in a triangle is pi.

Week 1 (2/1--2/5)

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.Went over basic definitions and concepts for Euclidean geometry. Listed and discussed Euclid's axioms and proofed Euclid's first theorem from the Elements.