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 Focusdirectrix definition of nondegenerate 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. NonEuclidean Geometry.
Recall Euclidean Geometry. §6.1 Poincare disk, dpoints and dlines. 
L29 
1123 
NonEuclidean reflections and transformations, Origin Lemma,
Axiom 5 
L30  
1125 
more examples §6.2 formula of NonEuclidean transformations §6.3 distance function 
L31  
13 
1128 
§6.3 distance function continued, midpoint, circle 
L32 
1130 
A nonEuclidean circle is a Euclidean circle in D examples of uncovered results 
L33  
1202 
review 

1208 
Final Exam 