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Axiomatic Geometry - Mathematics 360 - Fall 2002

List of Definitions, Axioms, Theorems

HW #    Due Date    Read Do
Final Exam Thu 12 Dec 2002    
25 Wed 4 Dec 2002   Conformal maps
24 Mon 2 Dec 2002 Sec 7.1, pages 313-321. p. 321: [9, 15, 17], 10, 11, 18-20.
23 Mon 25 Nov 2002   p. 179: [23, 24], 22, 25, 26. And figure out which of Theorems 3.9-4.21 hold in Neutral Geometry.
Quiz 6 Fri 22 Nov 2002 Covers HWs 18-22, and proofs of Theorems 4.17-4.19.  
22 Wed 20 Nov 2002 Section 4.3 pages 177-179 p. 179: [13, 16, 17, 19], 12, 14, 15, 18, 20, 21.
21 Mon 18 Nov 2002 Section 4.3 pages170-177 p. 179: [1, 3, 6], 2, 4, 5, 8-10.
20 Fri 15 Nov 2002   p. 168: [15, 17, 19, 20, 23], 16, 18, 21, 22, 24.
19 Wed 13 Nov 2002 Section 4.2 pages 164-168. p. 168: 11-14; + Prove the Triangle Inequality
Quiz 5 Fri 8 Nov 2002 Covers HWs 15-17.  
18 Wed 6 Nov 2002 Section 4.2 pages 156-164. p. 168: 1, 2, 5-10.(Do 6 and 7, and all of theorem 4.10, simultaneously, without considering cases! Hint: Ruler Axiom.) + Theorem 4.6 in NG
17 Mon 4 Nov 2002 Section 4.1 pages 150-154. p. 154: [11, 13], 12, 14, 15, 16, [17], 19, [21].
16 Wed 30 Oct 2002 Section 4.1 pages 143-150. p. 154: [1, 5], 3, 4, 6-8, 10.
Quiz 4 Fri 25 Oct 2002 Covers HWs 12-14, and problems 1-6 of HW 15, and proofs of Theorems 3.1, 3.3, 3.4.
(Proofs of Theorems 3.2 and 3.5 on Final Exam.)		  
15 Wed 23 Oct 2002 Section 3.2. p. 128: [3, 5], 1, 2, 4, 6, 8, 10-15, 17, 18.
14 Mon 21 Oct 2002 Read definition of Saccheri quadrilateral on page 115. p. 114: 9-15..
13 Fri 18 Oct 2002 Sec 3.1 pages 110-112. Re-read carefully proofs of Theorems 3.1-3.5. p. 114: 3-8.
12 Wed 16 Oct 2002 Sec 3.1 pages 103-110. p. 114: 1, 2.
Quiz 3 Fri 11 Oct 2002 Covers HWs 8-11.  
11 Wed 9 Oct 2002 Sec 2.4 pages 93-98. p. 98: 18, 20-23, [24, 25], + Q on Theorem 2.18. Extra Credit: see EC #7 below.
10 Mon 7 Oct 2002 Sec 2.4 pages 87-93. p. 98: 3-10, [11], 16.
9 Fri 4 Oct 2002 Sec 2.3 pages 76-80 (skip "Circumference of Earth"). p. 80: [27], 28-33. Extra Credit: 34.
8 Mon 30 Sept 2002 Read definition of convex on p. 66; and Sec 2.3 pages 68-75. p. 63: 20.  p. 80: [1-3, 5, 8], 4, 6, 9, 15-17.
Quiz 2 Fri 27 Sept 2002 Covers HWs 4-7 (but not sec 2.2, nor problems on p. 53).   
7 Wed 25 Sept 2002 Sec 2.1 pages 46-48. Sec 2.2 pages 51-53. p. 48: 19, 20, [22], 23, 26, 30;  p. 63: [1], [3], 4.
6 Mon 23 Sept 2002 Sec 2.1 pages 40-46. p. 48: 8, 12-18.
5 Wed 18 Sept 2002 Sec 2.1 pages 37-40. p. 48: 1-5.
4 Mon 16 Sept 2002 Sec 1.3 pages 29-31. Skim pages 32-33.
 p. 34: 19-22.
Quiz 1 Fri 13 Sept 2002 Covers all HW problems up to HW #3, plus proofs of Theorems 1.6 and 1.7 in section 1.3.  
3 Wed 11 Sept 2002 Sec 1.3 pages 26-29. p. 34: 6, 9, 10, 12, 15, 16, 18,  Q on Pasch
2 Fri 6 Sept 2002 Sec 1.2, and Sec 1.3 up to page 26. p. 20: 1-4; p. 34: 1-4.
1 Wed 4 Sept 2002 Skim Introduction. Read section 1.1. p 9: 6, 13-17.

Extra Credit Problems:

  1. Show if a triangle has two angle bisectors of the same length, then it is isosceles.
  2. Page 35 problem #17
  3. The Missing Strip Plane (an example of a "Euclidean Geometry" except that it doesn't satisfy Pasch's Separation Axiom (page 79 of "Geometry, a metric approach with models," by Millman and Parker).
  4. How can you estimate a ship's distance from the shore without ever walking more than one meter?
  5. Page 80 problem #34.
  6. Present in class the section on "Circumference of Earth," pages 75-76.
  7. Prove that if a grid of squares is rigid, then the segment marking algorithm will mark all the segments.

Square Brackets [ ]: It means this is an easy problem; you should do it, but we won't discuss it in class. If you have questions on it, ask me during office hours.

Updated: 31 August, 2009 17:44:19