- V. V. Prasolov, Non-Euclidean Geometry ---- (the paper copies of this book were distributed in class, thanks to the kind permission of the author and the publisher).
|Who is who
Preliminary course content (subject to change):
Michaelmas topics: Euclidean geometry, spherical geometry, affine and projective geometries;
Epiphany topics: Möbius transformations, hyperbolic geometry, further topics (geometric surfaces, discrete groups).
- Week 11: Möbius transformations, Inversion.
- Week 12: Inversion.
Möbius transformations and cross-ratios. Inversion in space and stereographic projection.
- Week 13: Stereographic projection. Conformal models of hyperbolic geometry (Poincaré disc). Problems class on Inversions and Möbius geometry.
- Week 14: Isometries of Poincaré disc. Circles in Poincaré disc. Upper half-plane model.
- Week 15: Elementary hyperbolic geometry: sine and cosine rules. Problems class on Poincare disc model.
- Week 16: Area of a triangle. Projective models of hyperbolic geometry: Klein model.
- Week 17: Hyperboloid model.
Types of isometries of hyperbolic plane. Problems class on computations in hyperbolic geometry.
- Week 18: More on isometries. Horocycles and equidistant curves. Discrete reflection groups.
- Week 19: Taming infinities with horocycles. Family of geometries: sphere-plane-hyperbolic plane. More on discrete groups acting on the hyperbolic plane. Problems class: computations in the Klein model.
- Week 20: Hyperbolic surfaces. Review via 3D hyperbolic geometry.
If you have any questions you are very welcome to ask (during the lectures, after a lecture,
during office hours, in any other convinient time or via e-mail)!!!
- There will be 4 sets of marked assignments during the term (to submit through Gradescope on Fridays by 5pm, weeks 14,16,18,20). --
- There will be also weekly unmarked sets of exercises. Please solve them timely!
Lecture Notes: (Epiphany matherial to be added during the term)
- Euclidean geometry: axioms (page 2) and basic theorems (pages 3-4), as well as the contact details on page 1.
Some tables to review the course:
If you find any mistakes/misprints in lecture notes, solutions or handouts, please let me know - Thanks!