# Approximate Schedule for Math 360

## Spring 2009

 Week Topics Reading Homework 1/27, 1/29 Administrivia. Introduction, Euclidean geometry. Chapter 1 Ch 1: 1,2,3,4. Major exercise 1. Exercises 8,9,10,11 (do not hand in). (due Thurs. 2/5) 2/3, 2/5 Incidence geometry. Chapter 2 Ch 2: 7, 9 (4th ed), 11, 13 (12 in 3rd ed). Major Exercise 5 (4th ed). (due Thurs. 2/12) 2/10, 2/12 Projective Geometry, Betweenness Axioms Chapter 3 (Betweenness) Ch 3: 1, 5, 6, 16 (17 in 3rd ed), 18 (19 in 3rd ed). (due Thurs. 2/19) 2/17, 2/19 Pasch & Crossbar Theorems, Congurence Axioms Chapter 3 (Congruence) No homework this week. 2/24, 2/26 No class on 2/24, Congruence continued. Finish chapter 3. Ch 3: 20, 24, 30, 35, major exercise 6. (due Thurs. 3/5) 3/3, 3/5 Continuity, Exterior angle theorem, SAS. First half of chapter 4. Ch 3: 26. Ch 4: 2 (9 in 3rd ed), 4 (11 in 3rd ed), 6 (13 in 3rd ed). (due Thurs. 3/12) 3/10, 3/12 Angle and Segment measure, Equivalence of Hilbert and Euclidean Parallel Postulates, Saccheri quadrilaterals. Chapter 4, through Saccheri-Lambert Quadrilaterals. Ch 4: 8 (21 in 3rd ed), 10 (4 in 3rd ed), 11 (5 in 3rd ed), 14, (due Thurs. 3/19) major exercise 5. (due Tues. 3/24) 3/17, 3/19 More on Saccheri and Lambert quadrilaterals, Angle sum of a triangle, the parallel postulate. finish ch 4. no homework. 3/24, 3/26 History of the parallel postulate. Midterm on Thursday, 3/26 chapter 5. midterms screw everything up. 3/31, 4/2 discuss midterm, Non-Euclidean Hilbert planes, defect and similarity, parallels with a common perpendicular. chapter 6. 4/7,4/9 Spring Break 4/14, 4/16 Limiting parallel rays, consistency of hyperbolic geometry. finish chapter 6, start 7. Chapter 5: 10, 13, 16. (due Thurs. 4/23) Chapter 6: 1 (don't hand in yet) 4/21, 4/23 Models of Hyperbolic geometry: Beltrami-Klein, Poincaré disk and half-plane. Power of a point, inversion in circles. Chapter 7. Chapter 6: 1, 2, 8, 12. Major exercise 6 (see these hints). (due Thurs. 4/30) 4/28, 4/30 SAS in the Poincaré disk model. chapter 7. Chapter 7: K-4, K-5, P-6, P-12. (due Thurs. 5/7) 5/5, 5/7 Elliptic geometry (briefly), review. Appendix A. Six Constructions for Extra-Credit (best tried in order): Euclidean: the midpoint of a segment, the tangent to a circle, and an octagon. Hyperbolic (Poincaré disk): an equilateral triangle, an inscribed quadrilateral, and a circumscribed quadrilateral. (due Wed. May 20) 5/19 Final Exam, Tuesday 5/19 at 11am in ESS 131 Review problems: In addition to the assigned homework problems, you should look at: Ch 2: 6, 8, 14a, 15a, and this problem. 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.