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Geometry I
(Winter 2017)


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.
Exercise sheets
 exercise sheet 13, due February 07
 exercise sheet 12, due January 31
 exercise sheet 11, due January 24
 exercise sheet 10, due January 17
 exercise sheet 09, due January 10
 exercise sheet 08, due December 20
 exercise sheet 07, due December 13
 exercise sheet 06, due December 06
 exercise sheet 05, due November 29
 exercise sheet 04, due November 22
 exercise sheet 03, due November 15
 exercise sheet 02, due November 08
 exercise sheet 01, due November 01
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, NonEuclidean Geometry, Math. Assoc. Amer.
 Cannon, Floyd, Kenyon & Parry,
Hyperbolic Geometry, from Flavors of Geometry, MSRI
 Martin, The Foundations of Geometry and the NonEuclidean Plane, UTM, Springer
 van Yzeren, A Simple Proof
of Pascal's Hexagon Theorem, Amer. Math. Monthly, 1993
 Henderson, Experiencing Geometry, Prentice Hall
Office Hours
