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
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Production
Scenes 1
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Scenes 3
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Exhibition
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Architecture and Tent Roofs

Fig 4. Olympic stadium in Munich with light-weight roof.

Minimal surfaces have special properties because of which they are used as models in several different fields. It is immediately apparent that the least area property was used in architecture for light roof constructions, form-finding models for tents, nets and air halls and which led to a new trend in architecture. Among the most spectacular buildings of that architectural style are the roofs of the Munich Olympic stadium and the former Kongreßhalle in Berlin, and also many of the smaller tent roofs on pavilions in parks and other public places. Famous architects like Frei Otto created minimal roofs worldwide.

In spite of their sometimes immense extension these roofs do not depress but instead stimulate the imagination with their winged and light shapes. If one ignores gravity then these roofs all have the form of gigantic soap films, which are spanned by the boundary and fixed at certain points. No other roofs could be constructed with similar shape but smaller surface area, and therefore the amount of material, and with it the roof's weight, is reduced to a minimum. Simultaneously, the balanced surface tension stabilizes the whole construction since the tension is in equilibrium at each point on the roof, as on a soap film.

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