| We ek |
Date | Contents | |
| 1 | 0905 |
Labour Day | |
| 0907 | outline, Euclidean geometry, overview and examples (Ceva and Pascal theorems, Apollonian circles, angular excess on sphere, angular defect on Poincare disk) | L1 | |
| 0909 |
Chapter 1. Conic sections
§1.1.1 Conics §1.1.3 Focus-directrix definition of non-degenerate conics |
L2 | |
| 2 | 0912 | §1.1.4 focal distance properties §1.1.5 conic sections are conics, proof by Dandelin sphere |
L3 |
| 0914 | §1.2.1 tangent lines §1.2.2 reflection properties of conic mirrors |
L4 | |
| 0916 | §1.2.2 continue §1.3 examples that quadratic curves are conics |
L5 | |
| 3 | 0919 | §1.3 writing a quadratic equation in standard form
|
L67 |
| 0921 | §1.3 finding the axes and vertices of a quadratic
equation |
L67 | |
| 0923 | Section 2.1 Euclidean geometry §2.1.1 What is Euclidean geometry? isometries, rotations |
L8 | |
| 4 | 0926 | §2.1.1 reflections, Euclidean transformations; group | L9 |
| 0928 | §2.1.1 examples of group properties of Euclidean
transformations §2.1.2 Euclidean congruence Chapter 2. Affine geometry §2.2.1 affine transformations |
L10 | |
| 0930 |
§2.2.1 affine properties and affine geometry §2.2.2 parallel projections |
L11 | |
| 5 | 1003 |
§2.2.2 a parallel projection preserves lines, parallel lines, and ratio of length along same direction §2.2.3 a parallel projection is an affine transformation; any affine transformation is a composition of two parallel projections |
L12 |
| 1005 |
MT1 |
||
| 1007 |
§2.2.3 application to conjugate diameters of ellipses §2.3.1 finding the equation of the image of a line under an affine transformation |
L13 | |
| 6 | 1010 |
Thanksgiving |
|
| 1012 |
§2.3.2 Fundamental Theorem of affine geometry §2.3.3 algebraic proof of basic affine properties; signed ratio |
L14 | |
| 1014 |
§2.3.3 more on signed ratio §2.4.2 Ceva's theorem |
L15 | |
| 7 | 1017 |
§2.4.3 Menelaus' theorem and example |
L16 |
| 1019 |
§2.5.1 conics have exactly 3 equivalent classes
§2.5.2 examples of affine properties of conics |
L17 | |
| 1021 |
§2.5.2 more examples Chapter 5. inversive geometry: overview §5.1 inversions |
L18 | |
| 8 | 1024 |
Formula for inversion, images of lines and circles,
a generalized circle is mapped
to a generalized circle |
L19 |
| 1026 |
angles and parallel lines
under inversion |
L20 | |
| 1028 |
§5.2 review complex plane; isometries on complex plane: notation, as compositions of reflections |
L21 | |
| 9 | 1031 |
scaling, inversion, linear and reciprocal functions, extended complex plane, stereographic projection |
L22 |
| 1102 |
stereographic projection preserves circles
and magnitude of angles §5.3 Inversive transformations, properties, and geometry. Moebius transformation. |
L23 | |
| 1104 |
composition and inverse of Moebius transformations,
associated matrices, the
Moebius group, an inversive transformation is either M(z) or M(\bar z)
|
L24 | |
| 10 | 1107 |
§5.4 Fundamental theorem of inversive geometry |
L25 |
| 1109 |
MT2 |
||
| 1111 |
Remembrance Day | ||
| 11 | 1114 |
how to decide whether 4 points belong to the same circle §5.5 Coaxal families of cirlces. Appolonian circles, algebraic proof. |
L26 |
| 1116 |
geometric proof, Coaxal circles theorem, relation between
inverse points and Appolonian circles |
L27 | |
| 1118 |
continue the proof of the lemma. Inverse points are
preserved under inversive transformations. Concentricity theorem. Note
we skip §5.5.4 |
L28 | |
| 12 | 1121 |
Chapter 6. Non-Euclidean Geometry.
Recall Euclidean Geometry. §6.1 Poincare disk, d-points and d-lines. |
L29 |
| 1123 |
Non-Euclidean reflections and transformations, Origin Lemma,
Axiom 5 |
L30 | |
| 1125 |
more examples §6.2 formula of Non-Euclidean transformations §6.3 distance function |
L31 | |
| 13 |
1128 |
§6.3 distance function continued, midpoint, circle |
L32 |
| 1130 |
A non-Euclidean circle is a Euclidean circle in D examples of uncovered results |
L33 | |
| 1202 |
review |
||
| 1208 |
Final Exam |