Computing distances in the Poincare disk model and upper half-plane model with Maple
| # | Date | Topic | Homework |
|---|---|---|---|
| 1 | W 1/28 | Conic sections (Topics from Ch 1) | - |
| 2 | F 1/30 | - | Assn 1: Problems 1-6, p. 7-10 (due 2/7) |
| 3 | M 2/3 | (no class) | - |
| 4 | W 2/5 | (no class) | - |
| 5 | F 2/7 | Introduction to the course | - |
| 6 | M 2/10 | (con't) | - |
| 7 | W 2/12 | Euclidean geometry from the transformation point of view (2.1) | Assn 2: p. 90: 2, 3, 4, 5. Also C1, C2 (due 2/17) |
| 8 | F 2/14 | - | - |
| 9 | M 1/17 | Classification of Euclidean isometries (Rees p. 14) | - |
| 10 | W 1/19 | The seven frieze groups (handout) | Assn 3: C3, C4, C5 (due 2/24) |
| 11 | F 2/21 | - | - |
| 12 | M 2/24 | Summarize Euclidean geometry via transformational viewpoint | Read Ex 1 p. 46 (and do problem 1 p. 90), see how ancient Greeks did this (http://aleph0.clarku.edu/~djoyce/java/elements/toc.html) |
| - | - | Introduction to projective geometry; the projective plane intuitively, perspectivity and projectivity of lines (3.1.1, 3.1.2, handout) | - |
| 13 | W 2/26 | - | - |
| 14 | F 2/28 | (No class today) | Assn 4: p. 90: 1, p. 147: 1 (top one), C6, C7 (due 3/7) |
| 15 | M 3/3 | 3.2 | - |
| 16 | W 3/5 | Projectivities are 3-fold transitive (handout) | Assn 5: p. 147: Section 3.2: 2, 3; Section 3.3: 1, 2, 3, 4 (due 3/12) |
| - | - | - | Last day to hand in assignments 1, 2, 3. (Henceforth late homework penalized 1/2 point per day) |
| 17 | F 3/7 | Cross ratio (3.5) | - |
| 18 | M 3/10 | - | - |
| 19 | W 3/12 | (Handout from "The Invention of Infinity") | Assn 6: p. 148 (Section 3.3): 5ab, 6; p. 149 (Section 3.5): 1a, 2, 3, 4 (due 3/26) |
| 20 | F 3/14 | Visit Art Museum | Assn 8: Vanishing points (due 4/8) |
| 21 | M 3/24 | Pappus' Theorem (p. 132) | Assn 7: Cross ratio sheet, Duality sheet, C8, and p. 150: 5 (due 3/31) |
| 22 | W 3/26 | Dual of Pappus (Brianchon's Theorem) | - |
| 23 | F 3/28 | Pascal's theorem and its converse (p, 184f.) | - |
| 24 | M 3/31 | Finite projective geometries | - |
| 25 | W 4/2 | Geometer's Sketchpad (handout) | - |
| 26 | F 4/4 | - | Midterm |
| 27 | M 4/7 | Non-Euclidean geometry (p. 261-65). Inversion (5.1.1) | - |
| 28 | W 4/9 | Inversion of lines and circles (5.1.2) | Assn 9: p. 257 (5.1): 1,2,3; p. 323 (6.1) 1, 2 (due 4/14) |
| 29 | F 4/11 | Straightedge and compass constructions (Handout from "Companion to Euclid") | - |
| 30 | M 4/14 | Inversion preserves angles (5.1.3) | - |
| 31 | W 4/16 | Distance in non-Euclidean geometry (6.3.1) | Assn 10: p. 323 (6.1): 4; p. 324 (6.3): 1, 2, 3. Also C10. (due 4/23). Note: C9 is extra credit (due 5/6) |
| 32 | F 4/18 | Computing distances in the disk model with Maple (see the top of this page) | - |
| 33 | M 4/21 | Non-Euclidean circles (6.3.3, p.289) | - |
| 34 | W 4/23 | The upper-half plane model H of hyperbolic geometry (6.5.3 p. 322) | - |
| 35 | F 4/25 | The relationship between inversions in C, non-Euclidean transformations in H, and projective transformations on its boundary. | - |
| 36 | M 4/28 | Distances and areas in H. The area of a trebly-asymptotic triangle. | Assn 11: p. 325 (6.4) #2. Also C12--C15 AND MORE (Due 5/6) |
| 37 | W 4/30 | The area of a hyperbolic triangle equals its defect. | - |
| 38 | F 5/2 | [no class] | - |
| 39 | M 5/5 | - | - |
| - | T 5/6 | [no class] | All homework and rewrites due today! (except for rewrites of homework which is returned Mon; these rewrites are due Fri 5/9) |