Touching Soap Films

An Introduction to Minimal Surfaces
By Hermann Karcher and Konrad Polthier


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Introduction
Plateau
History
Visualization
Architecture
Crystallography
Weierstraß
Properties 1
Properties 2
Properties 3
Symmetry
Alteration
Periodic
Handles
Production
Scenes 1
Scenes 2
Scenes 3
Results
Exhibition
Numerics
References
Web Links

Scenes from the Video I

Fig 16. Guided by the professor, Kalle explores the world of soap films. Video (3.5MB, 0.9MB)

The video contains topics on two levels. On the first level, it is a story about minimal surfaces intended for the general public. It is an introduction to the world of minimal surfaces which is understandable by pupils and students assuming no special scientific background. The video is suitable for school presentations giving the pupils an overview of the physical properties and applications of soap films, and a glimpse into the world of minimal surfaces as a classic and current research topic in mathematics.

Many of the geometric animations of the video come from recent mathematical research on minimal surfaces, some of which are new even for experts. This second level of understanding requires a deeper mathematical knowledge and makes the video an ideal complementary source of information for university courses in geometry and calculus of variations.

Architectural Buildings

Fig 17. A rubber band contracts to a shortest curve under the tension of the rubber molecules. Video (1.7MB, 0.4MB)

The amusement park shown at the beginning of the video contains a number of architectural constructions employing minimal surfaces. Some of the buildings simulate the type of roof used at the Olympic stadium in Munich in 1972, which is spanned between thick ropes. A real image is shown later in the palace. One other building is similar to the Institut für Leichte Flächentragwerke, the institute of the German architect Frei Otto, who is one of the most influential representatives of this architectural period of the 1960's and 1970's. Also shown is a rough model of the Berlin Kongreßhalle and different tent roofs, still frequently seen in parks worldwide.

© 1996-2013 Last modified: 23.04.2013 --- Konrad Polthier --- Freie Universität Berlin, Germany