Math 441 Assignments
Text: Stillman, Geometry of Surfaces
Week 1. 9/28-10/2
Read Chapter 1
Problems. Due Wed., 10/7
1.3.1, 1.3.3., 1.3.4, 1.3.5, 14.1, 1.4.2, 1.4.3, 1.5.2, 1.6.2, 1.6,4
Week 2. 10/5-10/9
Extra Session in THO 003
Monday 10/5 at 11:30 or Tuesday 10/6 at 2:30. Topic Composition of Isometries with The Geometer’s Sketchpad
No 12:30 class Friday, 10/9
Read Chapter 2, Sections 2.1 — 2.5
Problems. Due Wed., 10/16
2.3.1, 2.3.2, 2.3.3, 2.4.1, 2.4.2, 2.4.3, 2.4.4
Week 3. 10/12 - 10/16
Read Chapter 2, Sections 2.6 — 2.10
Problems. Due Wed., 10/21
2.5.2, 2.5.3, 2.6.2, 2.7.3, 2.74
Week 4. 10/19 — 10/23
Extra Session in THO 003
Monday 10/19 at 11:30 or Tuesday 10/20 at 2:30. Topic: Spherical Geometry with Sketchpad by means of stereographic projection
Read Chapter 3, Sections 3.1-3.6
Problems. Due Wed., 10/28
3.1.3, 3.2.1, 3.2.2, 3.3.2, 3.4.1, 3.4.2, 3.5.4, 3.5.5
Week 5. 10/26 — 10/30
Extra Session in THO 003
Monday 10/26 at 11:30 or Tuesday 10/27 at 2:30. Topic: Hyperbolic Plane
Read Chapter 3, Sections 3.7-3.10, Chapter 4, Sections 4.1-4.3
Problems. Due Wed., 11/4
4.2.1-6.
Week 6. 11/2 — 11/6
Extra Session in THO 003
Monday 11/2 at 11:30 or Tuesday 11/3 at 2:30.
No 12:30 class Friday, 11/6
Read Chapter 4.4-4.10
Assignment. Due Wed., 11/18
(1) Write up a proof of the formula relating the area of a spherical triangle with the angle sum.
(2) Prepare with Sketchpad or non-Euclid or graph paper, a couple of figures illustrating the effects of double line reflection in hyperbolic geometry. One figure for each of the 3 cases, intersection in the plane, at infinity, and no intersection.
(3) Prepare a one-page proposal, outline of your project. The final paper should be about 10 pages, with a bibliography, showing some individual "figuring-out" and synthesis on your part.
Week 7. 11/9 — 11/13
Wednesday 11/11 is a Holiday.
No 12:30 class Monday, 11/9 and Friday, 11/13
Assignment. Due