Schedule for Math 360

Fall 2009

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Week Topics Reading Homework
8/31, 9/4 Administrivia.
Introduction, Euclidean geometry. Start incidence geometry.
Chapter 1, Chapter 2 Ch 1: 1.
Ch 2: 7, 9 (4th ed), 11, 13 (12 in 3rd ed). (due Fri. 9/11)
9/7, 9/11 No class on Monday, 9/7.
Incidence geometry.
Chapter 2 Ch 2: 14, 15, Major Exercise 4, Major Exercise 5.
Think about Ch2 #18 but do not hand in. (due Friday 9/18)
9/14, 9/18 Projective Geometry, Betweenness Axioms Chapter 3 (Betweenness) Ch 3: 1, 5, 6, 15 (16 in 3rd ed), 18 (19 in 3rd ed). (due Friday 9/25)
9/21, 9/25 Pasch & Crossbar Theorems, Congurence Axioms Chapter 3 (Congruence) Ch 3: 17 (18 in 3rd ed), 20, 24, 35, major exercise 6. (due Friday 10/2) Also, try the following constructions: the midpoint of a segment and copying an angle.
9/29, 10/2 Continuity, constructible numbers, neutral geometry. Finish Chapter 3, start chapter 4. No written homework this week. However, you should do the following constructions: construct a perpendicular, an equilateral triangle in the hyperbolic disk, and an equilateral triangle in elliptic geometry.
10/5, 10/9 Alternate Interior Angle Thm, Exterior Angle Thm, Triangle Inequality. Chapter 4 Ch 4: 2 (9 in 3rd ed), 4 (11 in 3rd ed), 6 (13 in 3rd ed), 8 (21 in 3rd ed). (due Fri. 10/16)
10/12, 10/16 Angle and Segment measure, Equivalence of Hilbert and Euclidean Parallel Postulates, Saccheri quadrilaterals. Chapter 4, through Saccheri-Lambert Quadrilaterals. Ch 4: 10 (4 in 3rd ed), 11 (5 in 3rd ed), 14, major exercise 5. (due Fri. 10/23)
Here are the solutions.
10/19, 10/21 More on Saccheri and Lambert quadrilaterals, Angle sum of a triangle, the parallel postulate. finish ch 4. none due to midterm.
10/26, 10/30 Midterm on Monday, 10/26, discuss midterm, History of Parallel Postulate: Proclus, Clavius, etc. chapter 5. Chapter 5: 10(18 in 3rd ed), 13(21 in 3rd ed). (due Fri., Nov. 6)
11/2, 11/6 Wallis and similarity, Legendre and defect, more on similarity. chapter 6. Chapter 5: 6(10 in 3rd ed), 8(13 in 3rd ed), 14(22 in 3rd ed), 16(24 in 3rd ed). (due Fri., Nov. 13)
11/9, 11/13 Non-Euclidean Hilbert planes, defect and similarity, parallels with a common perpendicular. Limiting parallel rays, consistency of hyperbolic geometry. finish chapter 6, start 7. Chapter 6: 1(not in 3rd ed), 2(11 in 3rd ed), Major exercise 6 (see these hints). (due Fri. 11/20)
11/16, 11/20 Models of Hyperbolic geometry: Beltrami-Klein, Poincaré disk and half-plane. Power of a point, inversion in circles. Chapter 7.
11/23 SAS in the Poincaré disk model. (No class on 11/27) chapter 7. Chapter 7: K-4, K-5, P-6, P-12. (due Fri. 12/4)
11/30, 12/4 more on SAS. chapter 7. TBA
12/7, 12/11 stuff, nonsense Appendix A. TBA
12/16 Final Exam, Wed 12/16
at 2:15pm in Old Chemistry 144.
Review problems: In addition to the assigned homework problems, you might want to look at:
Ch 2: 6, 8, 14a, 15a.
Ch 3: 8, 9, 10.
Ch 4: 1, 3, 15, 17, 18, 19, 27.
Ch 5: 9, 14, 15.
Ch 6: 3, 4, 11.
Ch 7: K2, K3, P4.
Also, here is last spring's final.

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Page last modified on Tuesday, 8 December 2009 at 04:36 PM EST.