## 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. |

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Page last modified on Thursday, 14 May 2009 at 05:32 PM EDT.

Page last modified on Thursday, 14 May 2009 at 05:32 PM EDT.