TU Berlin Fakultät II
Institut für Mathematik

Arbeitsgruppe Geometrie



Geometry Group



Vergangene Semester


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Virtual Math Labs




Geometry I (Winter 2014/2015)

Lectures Boris Springborn Mon    12-14   MA 313
Mon 16-18 MA 313
Tutorials Isabella Thiesen Wed 10-12 MA 650
Thu 12-14 MA 848

This is a course of the Berlin Mathematical School held in English.


Non-euclidean geometry: spherical, hyperbolic, projective, Möbius, Lie, and Plücker line geometry.


In exercise 2 b) on sheet 4 you should solve for the coordinates of a right-angled triangle with angles and edge lengths taken from exercise 2 a).
There was a factor of 2 missing in one of the identities given as hints for ex 2.3, see updated version.
Here are some hints for the second exercise sheet. 
The first lecture will be October 13th.
The tutorials start in the second week (i.e. Wednesday, Oct 22nd).

Exercise sheets

Homework policy

  • To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments.
  • The exercises are to be solved in groups of two people.
  • The homework is due weekly at the beginning of the first lecture on Monday. Late homework is accepted only with a medical excuse.


There will be oral exams at the end of the semester.


For this course, there will be a book collection ("Semesterapparat") in the Mathematics Library on the first floor.
  • Lecture notes by Boris Springborn
  • V. V. Prasolov & V. M. Tikhomirov. Geometry. Translations of Mathematical Monographs, 200. American Mathematical Society, Providence, RI, 2001.
  • Nigel Hitchin's lecture notes on Projective Geometry.
  • Felix Klein. Vorlesungen über höhere Geometrie. Grundlehren der Mathematischen Wissenschaften, 22. Springer-Verlag, Berlin, 1968.
  • Wilhelm Blaschke. Projektive Geometrie. Birkhäuser, Basel, 1954.
  • Dmitry Fuchs & Serge Tabachnikov. Mathematical Omnibus: Thirty Lectures on Classic Mathematics. American Mathematical Society, Providence, RI, 2007. Preprint.
  • Marcel Berger. Geometry. I & II. Springer-Verlag, Berlin, 1987.
  • Michèle Audin. Geometry. Springer-Verlag, Berlin, 2003.
  • H. S. M. Coxeter. Non-Euclidean Geometry. Mathematical Association of America, Washington, DC, 1998.
  • J. W. Cannon, W. J. Floyd, R. Kenyon, R. Parry. Hyperbolic Geometry. In: S. Levy (editor). Flavors of Geometry. Mathematical Sciences Research Institute Publications 31. Cambridge University Press, Cambridge, 1997. Pages 59-115. Download PDF from the MSRI.
  • D. V. Alekseevskij, E. B. Vinberg, A. S. Solodovnikov. Geometry of spaces of constant curvature. In: E. B. Vinberg (editor). Geometry II. Encyclopedia of Mathematical Sciences 29. Springer, Berlin, 1993. Pages 1-138.
(This list is not ordered according to any relevant criteria.)

Office hours

Boris Springborn Wed 11-13 MA 871
Isabella Thiesen n.V.
n.V. MA 866

Isabella Thiesen . 27.01.2015.