# Math 618

(Last Updated May 25, 2022 @ 3pm)

## Materials

Course Notes (These notes are from Spring 2019, and so they are not a perfect representation of what we will do in class . But they are good guide nonetheless.)

Gradescope (for homework submsission)

Contact: You can always reach me via email at nicholas.vlamis@qc.cuny.edu. I will generally respond within 24 hours.

## End of the semester (5/16–5/23)

Monday, May 16 is the last day of class. We will spend the time working on problems from Assignment 12.

Exam 2 is on Monday, May 23 from 4-6PM and will be in our normal class room, 320 Kiely Hall.

Exam 2 will

*not*be cumulative; in particular, Exam 2 will cover the entirety of our notes on hyperbolic geometry.Exam 2 will be approximately the same length as Exam 1 and will consist of the same format, but with one notable exception:

**Please bring a graphing calculator to the exam**.You may bring two standard-sized sheets of notes to the exam. You may write on the front and back of the sheets.

I will hold my normal (virtual) office hour this week on Thursday from 4-5pm.

## Week 14 (5/9–5/13)

Discussed hyperbolic trigonometry, lambert quadrilaterals, and right-angled hexagons.Course Evaluations - Due by May 18 (Please fill them out!!)

Assignment 12 (not to be collected)

### Videos

This video should be watched *after* class on Monday, May 9 and *before* class on Monday, May 16.

Classify conformal hyperbolic rigid motions.

## Week 13 (5/2–5/6)

Proved the formula the area of a triangle in terms of its angles. Since many students were absent on account of the holiday, here is a link to the live video recording from last year's online course### Videos

These videos should be watched *after* class on Monday, May 2 and *before* class on Monday, May 9.

Prove that if two hyperbolic triangles are equiangular then they are congruent.

Prove that any triple of non-negative real numbers whose sum is less than pi can be realized as the angles of a hyperbolic triangle.

## Week 12 (4/25–4/29)

Proved that hyperbolic geometry is a non-Euclidean absolute geometry. Characterized hyperbolic reflections.### Videos

These videos should be watched *after* class on Monday, April 25 and *before* class on Monday, May 2.

## Week 11 (4/11–4/15)

Characterized all hyperbolic geodesics in the hyperbolic plane.### Videos

These videos should be watched *after* class on Monday, April 11 and *before* class on Monday, April 25.

## Week 10 (4/4–4/9)

Introduced the hyperbolic plane and showed that vertical line segments are geodesic.Exam 1 returned Wednesday, April 6

### Videos

These videos should be watched *after* class on Monday, April 4 and *before* class on Monday, April 11.

## Week 9 (3/28–5/1)

Exam 1 is on Wednesday, March 30

## Week 8 (3/21–3/25)

Reminder: Exam 1 is on Wednesday, March 30

### Videos

These videos should be watched *after* class on Monday, March 21 and *before* class on Monday, April 4.

## Week 7 (3/14–3/18)

Went over explicit examples computing images of lines and circles under inversions in a circle.### Videos

These videos should be watched *after* class on Monday, March 14 and *before* class on Monday, March 21.

## Week 6 (3/7–3/11)

Proved some basic properties about tangent lines to circles and recalled the definition of similar triangles and a basic proposition. ### Videos

These videos should be watched *after* class on Monday, March 7 and *before* class on Monday, March 14.

## Week 5 (2/28–3/4)

Proved that the composition of two distinct reflections is either a translation or a rotation.### Videos

These videos should be watched *after* class on Monday, February 28 and *before* class on Monday, March 7.

## Week 4 (2/21–2/25)

No class Monday, February 21 (college closed in observation of Presidents' day)

### Videos

These videos should be watched *after* class on Wednesday, February 23 and *before* class on Monday, February 28.

## Week 3 (2/14–2/18)

### Videos

These videos should be watched *after* class on Monday, February 14 and *before* class on Wednesday, February 23.

Video 5 (Notes) [This video is a recording of a live session with students, so there a few questions from students that I dress towards the end.]

## Week 2 (2/7–2/11)

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

These videos should be watched *after* class on Monday February 7 and *before* class on Monday, February 14.

## Week 1 (1/31–2/4)

Assignment 0 — Due Friday, February 4

*The Foundation's of Geometry*by David Hilbert (Of historical interest, not required)

Notes from Monday's Class (To be finished on Wednesday).

### 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).Introduce the notion of parallelism and establish the Euclidean theorems about parallel lines that hold for all absolute geometries.