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The Authors
This film is the result of the collaboration of three enthusiasts
who worked together on all aspects of the project.
Jos Leys Étienne Ghys Aurélien Alvarez
Engineer turned computer graphics enthusiast, specializing in mathematical imagery.
(Antwerp, Belgium)
CNRS senior researcher, working at the ENS-Lyon. He loves geometry. He was mainly responsible for the mathematics and the scenario. Graduate student at the ENS-Lyon. he was in charge of the technical aspects, and the computation of the images.

For their generosity, we thank:
Florent Ghys

interprets his compositions:

Laurine 4
Bricole anticyclonique
Cinq pianos
Canon a4 perpetuus
(J.S.Bach, arrangement)
l'Air du baobab
Laurine 8
John Lewis Grant

Interprets some pieces of  the

Well Tempered Clavier I by J.S.Bach:

Fugue 8 in D-sharp minor (BWV 853B)
Fugue 4 in C-sharp minor (BWV 849B)
Prelude 1 in C Major (BWV 846A)
Prelude 4 in C-sharp minor (BWV 849A)
Prelude 22 in E-flat minor (BWV 867A)
Prelude 7 in E-flat Major (BWV 852A)
Kevin McLeod

interprets his compositions:

Long note One
Trio for piano, cello and clarinet
Majestic Hills

and interprets

Sheep may safely graze (BWV 208)

Canon in D major

Waltz (OP.40)

Damien Gaboriau and Étienne Ghys  (French)
Shaun Bullet, Matt Delong  and John Guaschi (English)
Adolfo Guillot and Alberto Verjovsky (Spanish)
Mohammed Laid Kadri  (Arabic)
  Andreas Lochmann and Daniel Pape (German)
Claudio Vailati and Lilli Fragneto (Italian)
George Shabat (Russian)
Takashi Tsuboi (Japanese)

Recorded at the Service Commun Audiovisuel et Multimédia of the ENS-Lettres et Sciences Humaines, Lyon,
 in Cuernavaca (Mexico) , at Tokio University (Japan), at Taylor University (Indiana, USA), in Moscow (Russia),
 at the Mathematisches Institut der Georg-August-Universität Göttingen (Germany), in Milan (Italy) and in Algiers (Algeria).
Thanks to the Video Archives Committee of the Graduate School of Mathematical Sciences, the University of Tokyo.

With thanks to Kevin BradleyKevin Gehrett, Serge Dubov, Andreas Thom.

Image computation
was done at the Pôle Scientifique de Modélisation Numérique (PSMN) of the ENS-Lyon

Special thanks to

Hervé Gilquin and Gérard Lasseur

Most of the images were created in Povray
Fractal images were created in Ultrafractal

We also thank

Damien Gaboriau

for the support  by the Unité de Mathématiques Pures et Appliquées (UMPA) of the ENS-Lyon
The making of this DVD was facilitated by a subsidy of the École Normale Supérieure de Lyon.
Thanks to our translators
Alciléa Augusto
Paolo Bellingeri
Dietmar Bisch
Grant Cairns
Michael Drzal
Sorin Dumitrescu
Jan Dusatko
Michael Eisermann
Louis Funar
Étienne Ghys
Alexei Glutsyuk
John Guaschi
Adolfo Guillot
Li Huili
Vladimir Jaksic
Leila Khatami
Victor Kleptsyn
Konstantinos Konstantoudakis
Boštjan Kuzman
Jos Leys
Martin Lustig
Greg McShane
Gilza de Melo
Mirsad Muharemagic
Klaus Niederkrueger
Melek Önen
Patrick Popescu
Ana Rechtman
Daniel Rosen
Boubaker-Khaled Sadallah
Pedram Safari
Vlad Sergiescu
Tan Lei
Takashi Tsuboi
Alexei Tsygvintsev
Jeff Weeks
and to the translators of the website:
Hamid Abchir 
Concepción Abraira (Chiti)
José Angel
Alciléa Augusto
Artem Bukhonov
Anna Bykhovskaya
 Grant Cairns
Felipe Cano
Jerry Cheng
Benson Farb
Bruno Gimeno
Natalia Goncharuk
Roman Ilushchenko
Hamza Khelif
Mikhail Khristoforov
Victor Kleptsyn
Yury Kudryashov
Eric Kuhnt
Andreas Lagotzki
Javier Lopez
Juan José Madrigal Martínez
Gilza de Melo
Karla Olvera
Adriana Portillo
Diego Ramirez
Simon Schliesky
Hamish Short
Ferran Valdez
Karen Vogtmann
Amie Wilkinson
Yang Ziqing
For hosting the files as mirror sites we thank:
The Povray organisation
Tokyo University, Japan
Instituto de Matemáticas, UNAM, Unidad Cuernavaca México
Institute of Mathematics, Beijing, China
Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brasil 

For their advice and comments, we thank
Thierry Barbot
Vincent Beffara
Marc Bernot
Jos Boogen
Vincent Borrelli
Claude Bruter
Jean-Paul Delahaye
Élise Ghys
Pauline Gonnaud
Antonin and Stéphanie Guilloux
Jean-Pierre Kahane
Silvio Levy
Salim Mokrane
Philippe Saade
Jérôme Surroca
Francis Trincaretto
Frank Verheyen
Abdelghani Zeghib

A special thank you to our presenters
Hipparque : mathematician, geometer...

Ludwig Schläfli : the discoverer of the fourth dimension

Bernhard Riemann : pure genius

Heinz Hopf : topologist

Maurits Cornelis Escher : artist  and géometer

Adrien Douady : an unforgettable master

To Gilberte and Martine...