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Special Topics:Differential Geometry

8snails by George Francis

Blaine Lawson's class \tau of ruled, minimal surfaces on S^3 have this quaternionic parameterization: u,v -> e^{2iu}cos v + j e^{biu}sin v which can yield the untwisted annulus, spherical bead, half-twisted Moebius band, Sudanese Moebius band, once-twisted annulus, Clifford torus, three-half-twisted Moebius band, and Brehm's smooth knotbox.

How to make it: based on the soloRTICA called illiSnail in /u/gfrancis.

Image created: January 1993


Copyright © January 1993 by The Geometry Center, Univerity of Minnesota. All rights reserved.
For permission to use this image, contact permission@geom.umn.edu.

External viewing: small (100x100 5k gif), medium (500x429 55k gif), or original size (1792x1536 1,450k tiff).

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Created: Sat May 22 23:17:48 CDT 1999 --- Last modified: Sat May 22 23:17:48 CDT 1999