In this section we introduce some of the mathematical background that lie behind the pictures and installations of IMAGINARY. For beginners and Maths-newcomer, for people with keen interest and advanced learners, on this page you will find different types of articles and links. We wish you a good time discovering and exploring algebraic geometry, differential geometry, chaos theory, dynamic flow, etc.

Background articles have been written by experts for IMAGINARY. Mathematical concepts and applications of algebraic geometry are introduced catering different levels of mathematical knowledge. Please note that some articles are available in German, others in English only.

The two following articles show, how the Moebius strip and the trefoil knot can be constructed using algebraic equations, for example through the programme SURFER. Only elementary methods are used such that the proofs are also accessible to graduate math work groups for pupils in secondary schools.
Author: Stefan Klaus, Mathematisches Forschungsinstitut Oberwolfach
Description: Moebius strip, trefoil knot, SURFER
Download article on Moebius strip (PDF 580 KB, ENGLISH)
Download article on trefoil knot (PDF 1.4 MB, ENGLISH)

Author: Duco van Straten, Johannes Gutenberg-University Mainz
Description: ein schöner, bebilderter Überblick zur algebraischen Geometrie
Download article (PDF 4.8 MB, GERMAN)

Author: Herwig Hauser, Vienna University
Description: an small and entertaining introduction to singularit theory
Downlaod article (PDF 140KB, GERMAN)

Author: Oliver Labs, University of the Saarland
Description: an appealing mathematical introduction to surfaces and singularities, High-school level
Download article (PDF 1.3 MB, GERMAN)

Author: Jürgen Richter-Gebert, Technical University Munich
Description: understandable for everyone, introduction to mirrors, symmetries and chaos
Download article (PDF 2.7 MB, GERMAN)

Two pictures of the IMAGINARY exhibition are very spezial. They show images that look like knots. Actually their creation depends on prime numbers. A visual introduction to these images is given by Jos Leys and Etienne Ghys in an article of the American Mathematical Society.
Authors: Jos Leys und Etienne Ghys
Description: Lorenz and Modular Flows: A Visual Introduction
Article on the AMS website

www.algebraicsurface.net
A collection of links to websites, pictures and programs connected to the visualization of algebraic surfaces.