| Week | Date | Contents |
| 1 | 0906 |
Labour Day |
| 0908 | Outline Introduction: Ceva and Pascal's theorems, Parellel Postulate and non-Euclidean geometry |
|
| 0910 | §1.1.1 Conic sections §1.1.3 Focus-directrix definition of non-degenerate conics |
|
| 2 | 0913 | §1.1.4 Focal distance properties of ellipse
and hyperbola §1.1.5 Every conic section is a conic: proof by Dandelin sphere |
| 0915 | * Every conic is a conic section §1.2.1 tangent lines §1.2.2 Reflection properties (statement) |
|
| 0917 | §1.2.2 proof of reflection properties §1.3 Recognizing conics |
|
| 3 | 0920 | §1.3 An example §1.4.1 Quadric surfaces |
| 0922 | §1.4.1 graphing of nondegenerate quadric surfaces in
standard forms §1.4.2 Recognizing quadric surfaces |
|
| 0924 | §1.4.3 a hyperboloid of one sheet is a ruled surface |
|
| 4 | 0927 | §2.1.1 Isometries and Euclidean transformations of R^2 |
| 0929 | §2.1.1 examples; isometries and Euclidean transformations of R^2 are the
same |
|
| 1001 |
§2.1.2 Euclidean transformations of R^2 is a group,
examples Appendix 1. definition and examples of group §2.1.2 Euclidean congruence of figures |
|
| 5 | 1004 |
§2.1.2 Equivalence relation and equivalence
class §2.2.1 Affine transformations and affine properties §2.2.2 parallel projection |
| 1006 |
MT1 |
|
| 1008 |
§2.2.2 Parallel projections preserve lines, parallel lines
and ratio of length along the same line. §2.2.3 Parallel projections are affine transformations. Each affine transformation is a composition of two parallel projections, and hence also preserves lines, parallel lines and ratio of length along the same line. |
|
| 6 | 1011 |
Thanksgiving |
| 1013 |
§2.2.3 application to conjugate diameter of ellipses §2.3.1 finding images of lines §2.3.2 the affine transformation mapping (0,0), (1,0), (0,1) to any 3 non-collinear points |
|
| 1015 |
§2.3.2 The fundamental theorem of affine geometry
§2.3.3 affine transformations preserve signed ratio of lengths on parallel lines §2.4.2 Ceva's theorem: statement and first proof |
|
| 7 | 1018 |
Ceva's
theorem: application and second
proof §2.4.3 Menelaus theorem: statement, first proof, and application |
| 1020 |
§2.4.3 second proof §2.5.1 three affine-congruent classes of non-degenerate conics, center of ellipse/hyperbola is an affine concept |
|
| 1022 |
§2.5.1 tangent lines and asymptotes of conics are affine
objects
§3.1.1 perspectivity from artist's viewpoint |
|
| 8 | 1025 |
§3.1.2 imagies of lines under perspectivities, vanishing
points §3.1.3 Desargues' theorem |
| 1027 |
§3.2.1 and §3.2.2 Projective points and lines |
|
| 1029 |
§3.2.2 intersection Point of Lines §3.2.3 embedding planes |
|
| 9 | 1101 |
§3.3.1 projective transformations
§3.3.2 image of Line under proj. transf. |
| 1103 |
§3.3.2 example §3.3.3 is skipped §3.3.4 proj. transf. from reference Points to arbitrary 4 Points |
|
| 1105 |
§3.3.4 Fundamental Theorem of Projective Geometry §3.4.1 Application: proof of Desargues' Theorem |
|
| 10 | 1108 |
§3.4.2 Pappus and Brianchon's theorems, duality §3.5 cross ratio |
| 1110 |
MT2 |
|
| 1112 |
§3.5 examples and theorems |
|
| 11 | 1115 |
§3.5 cross ratio of the intersection points of a pencil of 4 lines with a cutting line is independent of the cutting line; unique fourth point theorem; Pascal's theorem for a circle (statement) |
| 1117 |
Proof of Pascal's theorem Chapter 4 sketch: projective congruence of conics, three tangents theorem and Pascal's theorem for conics |
|
| 1119 |
§5.1 overview of Chapter 5, inversions
|
|
| 12 | 1122 |
§5.1 image of lines, circles, and angles
under inversions
|
| 1124 |
§5.2 transformations of the extended complex
plane |
|
| 1126 |
§5.2 reciprocal and linear functions are
composition of inversions §5.2.4 Stereographic projection: formulas, it maps circles to generalized circles and preserves angles |
|
| 13 |
1129 |
§5.3 inversive transformations, Moebius
transformations |
| 1201 |
Sketch of Non-Euclidean and spherical geometries (Chapters 6 and
7) |
|
| 1203 |
review |
|
| 1214 |
Final Exam |