MAA Found Math for the Week of January 23, 2012
MAA Found Math: "Lawson's Minimum-Energy Klein Bottle" by Carlo H. Séquin (EECS Computer Science Division, University of California, Berkeley) was awarded Third Place at the Exhibition of Mathematical Art during The 2012 Joint Mathematics Meetings in Boston. Double click the image for full size. Read the full press release.
According to the Exhibition's catalog:
"This is a gridded model of a Klein bottle (Euler characteristic 0, genus 2) with the minimal possible total surface bending energy. This energy is calculated as the surface integral over mean curvature squared. States Séquin, "My professional work in computer graphics and geometric design has also provided a bridge to the world of art. In 1994 I started to collaborate with Brent Collins, a wood sculptor, who has been creating abstract geometrical art since the early 1980s. Our teamwork has resulted in a program called “Sculpture Generator 1” which allows me to explore many more complex ideas inspired by Collins’ work, and to design and execute such geometries with higher precision. More recently I have become interested in mathematical and topological concepts such as the regular homotopies that permit immersions of a torus or a Klein bottle to be smoothly transformed into other shapes in the same class. I then try to turn the mathematical models that illustrate these concepts into aesthetically pleasing sculptural maquettes."
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