Dates | Material Covered |
1/20 |
Introduction to the Course Preface: p. ix Ch. 0: pp. 3-4 Ch. 1: pp. 8-11 Lecture 1 |
1/25-1/27 |
Axioms and Proof Section 1.2 - Theorem 1.4.3 Lecture 2 Lecture 3 Homework 1/25: Post a question about the proof on page 15. Homework 1/27: Explain why a combination of two isometries (e.g. a translation followed by a rotation) is still an isometry. |
2/1-2/3 |
Sections 1.4-1.6 Lecture 4 Homework 2/1: Post an answer to one of the questions about page 15. Do exercise 1.15. Bonus 1.13(SAS) Lecture 5 |
2/8-2/10 |
Section 1.6
Lecture 6 Homework 2/8: Exercise 1.23 (explain your reasoning, but a formal proof is not required), 1.24 (You may assume that the result of Exercise 1.14 (ASA) is true.) Section 1.6, review for Test 1, symmetries of plane patterns. 2/10: Snow day. |
2/15-2/17 |
President's Day holiday Review for Test 1 Bring scissors, tape, and red and blue pens to class. |
2/22-2/24 |
Test 1 Section 1.7 Homework 2/24: Referring to Figure 1.17, prove that if B' and C' are midpoints of their respective edges, then line B'C' is parallel to line BC. Lecture 7 |
3/1-3/3 |
Angle Vocabulary Lecture 8 Lecture 9 Section 1.9 |
3/8-3/10 | Spring Break |
3/15-3/17 |
Lecture 10 Project Proposals Due 3/15 Straightedge and Compass Construction Homework due 3/17 Lecture 11 |
3/22-3/24 |
Lecture 12 Lecture 13 Straightedge and Compass Construction Homework due 3/24: Exercise 3.1. Hint: Think about what happens if you repeat the construction from Theorem 3.2.2 with O and S as the base points. |
3/29-3/31 |
Straightedge and Compass Construction Lecture 14 Review for test Test 2 3/31 |
4/5-4/7 |
Lecture 15 Lecture 16 Homework due 4/7: Read pages 196 and 223-224. Post a question about the reading to the message board, or explain why you think some familiar theorem from plane geometry is not true in spherical geometry. Spherical Geometry |
4/12-4/14 |
Homework due 4/12: Is it true that the perpendicular bisector of a spherical segment
AB is exactly the set of all points P for which |AP| = |BP|? Prove this or discuss why you
cannot. (Hint: See Lecture 14.) Lecture 17 Lecture 18 Hyperbolic and Taxicab Geometry Homework due 4/12: (Extensions available on request.) Read pages 122-124. Post a question to the message board or respond to a classmate's question. (Your response need not be an answer, but it should at least expand on the question you responded to.) Sections 5.1-5.3 |
4/19-4/21 |
Patriot's Day holiday Project due 4/21 Lecture 19 Taxicab and finite geometry |
4/26-4/28 |
Lecture 20
Test 3 review. Test 3 Late homework due 4/28 |
5/3-5/5 |
Review for Final: Study proof of side-side-side, Euclid's axioms, axiom equivalence, triangle
congruence, similar triangles, Star Trek Lemma, construction and proofs related to construction,
definitions in spherical geometry, differences between spherical, plane and hyperbolic geometry. Cumulative Final Exam: May 5, 11-1 Test redo due 5/5 |