John Oprea's Soap Film Page
Soap films provide a wonderful tool for establishing a link between
mathematics and science. The mathematics behind soap films and bubbles
is a beautiful mixture of differential geometry, the calculus of variations
and complex analysis. The science behind soap films revolves around the
subject of surface tension --- a property which influences even our
everyday lives (e.g. washing clothes!). Below there are links
to some soap film pages, but I would love to hear from you if you know
of others! I taught a course, The Mathematics and Science of Soap Films
and Bubbles (Fall 1998), and the material from that course has now
appeared in the American Mathematical Society Student Library series under the
title,
The Mathematics of Soap Films: Explorations with Maple.
--- Review on MAA
Online by Helen Moore
The book consist of chapters on surface tension, differential
geometry and complex variables, minimal surfaces and calculus of variations
as well as a large chapter containing Maple worksheets with procedures
pertaining to these subjects. For example, the Maple worksheets show
how fused bubbles arrange their angles and how liquids rise under
capillary action. Of course, the subject is mathematical as well and
this involves the study of minimal surfaces.
Minimal surfaces --- the mathematical version of soap films --- may be
created by using complex variables in the form of the so-called
Weierstrass-Enneper representation. Maple can be used to automatically
calculate the Weierstrass-Enneper representation and then plot the
surfaces created in this way. This is all done in the book, but
in a way that should be accessible for upper level undergraduates. Click
on the following to see some of the things Maple can do.
PPT,
PDF,
WMV
The following links explore different aspects of films and bubbles as
well as other things involving geometry such as knots, fluid flow and
shape evolution.
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