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401-2534-00L 6 Credits BSC D-MATH
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Geometry

Geometrie

Lecturers & Examiners: Prof. Dr. Tom Ilmanen
VVZ CR n/a

Last Updated: 2026-02-05 16:22:17

Abstract

The course will treat Möbius transformations and hyperbolic geometry.

Objective

Theorems, proofs, techniques, calculations, pictures, software and examples in geometry.

Content

Isometry groups; hyperbolic plane; parallels and ultraparallels; getting lost; games and apps; stereographic projection, Möbius transformations, cross ratio; Poincare model, metric, isometries, geodesics, distances; upper half-plane model, ideal triangles, angle-excess formula; Klein model; Minkowski space model; comparisons to spherical and flat geometry; no embedding in R^3; stars appear farther, tidal forces, dangers; possibly compact hyperbolic surfaces, Gauss-Bonnet formula, tesselations, trees.

Resources

Learning Materials (Links)

General Information

Language
English
Levels
BSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 20 minutes

Course Components

Type Title Time & Place Hours
lecture Geometrie
  • Tue 11:15-12:00 (HG D 3.2)
  • Thu 14:15-16:00 (HG G 5)
3 h weekly
exercise Geometrie
Groups are selected in myStudies.
  • Mon 16:15-18:00 (HG D 3.2)
  • Mon 16:15-18:00 (HG F 5)
  • 03.05 Date 16:15-18:00 (HG F 26.3)
  • 31.05 Date 16:15-18:00 (HG F 26.3)
2 h weekly

Offered In