TU Berlin Fakultät II
Institut für Mathematik

Geometry I (WiSe 17)



Geometry Group



Vergangene Semester


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Geometry I

(Winter 2017)

Lectures Prof. Dr. John Sullivan Wed 08-10 MA 141
Thu 12-14 MA 376
Tutorials Jan Techter Wed 10-12 MA 548
Wed 14-16 MA 548

This is a basic course of the Berlin Mathematical School and will be held in English. Depending on the audience one of the tutorials may be held in German.


Introduction to projective, spherical, hyperbolic, Möbius and Lie geometry.


[2018, June 7]
Update: Further oral exams will be offered on 26 June. Please see Prof. Sullivan's webpage.
[2018, February 06]
Correction on exercise sheet 13, exerice 2:
The signatures for the first two pencils of circles were reversed.
[2018, January 16]
Correction on exercise sheet 10, exerice 4:
The hyporbolic line $l_3$ should be defined by the properties $l_1 \perp l_3$ and $l_2 \perp l_3$
and the normals should be normalized to satisfy $\langle n_1, n_1 \rangle = \langle n_2, n_2 \rangle = 1$.
[2018, January 05]
Correction on exercise sheet 09, exerice 2:
The angle $\alpha_n$ in (ii) is the interior angle of a regular Euclidean $n$-gon as determined in (i).
[2017, October 13]
First lecture on Wednesday, October 18.
First tutorials on Wednesday, October 25.

Exercise sheets

Homework policy

  • To get a certificate for the tutorial, you need to satisfactorily complete 60% of the homework assignments.
  • The exercises are to be handed in in groups of two people. Depending on the number of students it might be possible to form groups of three.
  • The homework is due weekly during the tutorials on Wednesday.


  • Springborn, lecture notes from the 2007 version of this course at TU Berlin
  • Bobenko, lecture notes (projective geometry) from the 2016 version of this course at TU Berlin
  • Euclid, Elements: online with java or Greek beside English text
  • Prasolov & Tikhomirov, Geometry, TMM 200, Amer. Math. Soc.
  • Hitchin, lecture notes on Projective Geometry: Chapters 1&2,   3,   4,   5
  • Fuchs & Tabachnikov, Mathematical Omnibus
  • Klein, Vorlesungen über höhere Geometrie, GMW 22, Springer
  • Blaschke, Projektive Geometrie, Birkhäuser
  • Berger, Geometry I & II, Springer
  • Audin, Geometry, Springer
  • Coxeter, Non-Euclidean Geometry, Math. Assoc. Amer.
  • Cannon, Floyd, Kenyon & Parry, Hyperbolic Geometry, from Flavors of Geometry, MSRI
  • Martin, The Foundations of Geometry and the Non-Euclidean Plane, UTM, Springer
  • van Yzeren, A Simple Proof of Pascal's Hexagon Theorem, Amer. Math. Monthly, 1993
  • Henderson, Experiencing Geometry, Prentice Hall

Office Hours

Prof. John Sullivan Tue 13-14 MA 802
Jan Techter Mon 14-15 MA 883

Jan Techter . 07.06.2018.