# 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.