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The Struik Sequence: the Klein Bottle, the Temple of Viviani, and Evolute Stripes

For the hundredth birthday of Professor Dirk J. Struik, a group of undergraduate students worked with the artist to produce still images and video from the area of differential geometry.

The first video image shows the slices of an ordinary sphere by a family of cylinders around an axis not going through the center of the sphere. The position where one line on the cylinder goes through the origin while the cylinder and the sphere have a common tangent plane at another point is a classic configuration known as The Temple of Viviani, named for the fifteenth century mathematician who studied its properties. The animation presented here was executed by Ying Wang.

The second image on the videotape is a projection of The Klein Bottle into three-space, rendered in semi-transparent glass supported by metal bands, with a fly-through sequence and music created by Jeff Beall. The single image demonstrates the way the Klein bottle can be fashioned from tubes around pieces of figure eight curves.

The third image shows a red helicoidal strip and its two green and purple evolute surfaces, the collection of focal points where the surface would intersect itself when pushed far enough along its normal directions.

Surfaces Beyond the Third Dimension
Last modified: 08 Oct 2000 08:47:32
Comments to: Thomas F. Banchoff
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