Non-Euclidean Geometry

Instructor

Jeremiah Heller (jbheller at illinois)
362 Altgeld
Office hours: Monday 1-1:50, Tuesday 2:00-2:50.

Lecture

Section F13 at MWF 2:00-2:50 in 140 HENRY BLD

Syllabus

The course syllabus can be found here.

Announcements

Some review problems for the final exam are here and some solutions here.

Exam 3 solutions.

Some review problems for Exam 3 are here and some solutions are here.

Exam 2 solutions.

Some review problems for Exam 2 are here and solutions here.

Exam 1 solutions.

Some review problems for Exam 1 are here and some solutions are here.

Worksheet from [2/5] can be found here and solutions here.

Download and install the Geometry Explorer software here. For fun and to get used to the software, you could do Project 1 in 1.3 of the text (no project report will be collected).

Assignments

Homework 9 (due 4.25): 8.2.10, Extra Credit: 8.6.6 .

Project: Do Project 11 in 7.7 of the text. You don't have to do the exercises or write a report yet.

Homework 8 (due 4.13): 8.2.9, 8.2.11, 8.2.13, 8.3.1, 8.3.4

Homework 7 (due 4.6): 3.5.6, 3.5.7, 3.5.8, 7.5.9, 7.5.11, 7.6.2

Homework 6 (due 3.9): 5.2.4, 5.2.12, 5.4.6, 5.4.9

Project Report 3 (due 3.9): Do Project 10 in 7.4. Include with the report 7.4.1, 7.4.2

Reflection 2 (due 3.2): Do 5.2.5 and 5.3.1.

Homework 5 (due 3.2): 7.3.1, 7.3.2, 5.1.2, 5.1.5, 5.1.6

Homework 4 (due 2.24): 7.2.1, 7.2.3, 7.2.4

Project Report 2 (due 2/24): Write up the project report for Project 4 (in 2.7 of the text). For the report, include a brief analysis of the constructions used in the project and Exercises 2.7.1-2.7.3.

(due 2/17) Do Project 4 (in 2.7 of the text) on circle inversion and orthogonality. You don't have to write a report on it yet.

Homework 3 (due 2/10): 2.1.4, 2.1.6, 2.1.9, 2.2.7, 2.5.3

Reflection Piece 1 (due 2/10): see here.

Homework 2 (due 2/3): 1.5.4, 1.5.5, 1.5.6.

Project Report 1 (due 2/3): Do project 2 in Chapter 1.7 as described in the text (i.e. for hyperbolic geometry) and then repeat for spherical geometry (File -> New -> Spherical). Your report will consist of a comparison of Euclidean, hyperbolic, and spherical geometries together with Excercise 1.7.1 for both hyperbolic and spherical geometries. Note: No proofs are needed for 1.7.1, only a discussion of the results from your experiments with Geometry Explorer. (See Exercise 1.6.7 for the definition of the spherical geometry.)

Homework 1 (due 1/27): 1.4.3, 1.4.4, 1.4.5.