Architecture and Mathematics: Soap Bubbles and Soap Films

Michele Emmer ()
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Michele Emmer: Sapienza Università di Roma, Dipartimento di Matematica

Chapter Chapter 77 in Architecture and Mathematics from Antiquity to the Future, 2015, pp 449-458 from Springer

Abstract: Abstract Plateau’s problem consists in taking a generic curve in three-space and finding a surface with the least possible area bounded by that curve. The empirical solution may be obtained by dipping a tridimensional model of the curve into soapy water, resulting in a form called a minimal surface. When a soap bubble is blown, the soapy surface stretches; when blowing ceases, the film tends toward equilibrium. Frei Otto used soap film models to design his tensile-structures, developing a technique to obtain a precise photogrammetric evaluation of soap film models and another method to simulate peaks in a membrane of soap films. H.A. Schwarz solved Plateau’s problem for a non-plane boundary by developing the periodic minimal surface. Infinite periodic minimal surfaces, combinations of saddle polygons or surfaces, are more stable. Such a surface has been adapted as a play sculpture in the Brooklyn Museum, where children can actually enter into the labyrinthic structure of periodic minimal surfaces.

Keywords: Minimal Surface; Soap Film; Soap Bubble; Plateau Problem; Soapy Water (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-00143-2_30

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DOI: 10.1007/978-3-319-00143-2_30

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