Fakultät II
Institut für Mathematik

# Geometry I (WiSe 17)

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# Geometry I

## (Winter 2017)

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

### Contents

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

### News

[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.

### 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.

### Literature

• 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.