Utah State University
Prospects in Mathematics 10/06/04

Undergraduate Lecture
on
The Mathematics of Soap Films



In October 2004, I was honored to be the Utah State University Prospects in Mathematics lecturer. The first lecture was for an undergraduate audience and it was about the Mathematics of Soap Films. We did experiments with films illustrating various mathematical and physical principles. Also, we talked about the mathematics needed to understand soap film geometry: differential geometry and complex variables. Finally, we showed how Maple can be used to create new minimal surfaces according to the Weierstrass-Enneper Representation and how Maple can solve differential equations (explicitly and numerically) to give us shapes.These are photos from the lecture, all taken by Nancy Smart of the Utah State Math Department. Thanks to Nancy and to all of the "volunteers" for their help with the experiments! Finally, thanks to my host Dariusz Wilczynski and Utah State for the invitation to speak and for the chance to see a beautiful part of the country.

















Dariusz Wilczynski





Pepper held up by Surface Tension





Pepper held up by Surface Tension





Soap films do work





Soap films minimize area: A catenoid





Another catenoid





Soap films minimize area: A helicoid





Circles maximize area subject to fixed perimeter





Plateau's Rules




What has he been drinking?




Is this a flattering view?





Talking





More talking





Even more talking





Will it end?





Bear Lake





Dariusz again


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