DPVC (CV/Art)

The Two-Piece Property These are two images created for an article by Thomas Banchoff and Wolfgang Kühnel that surveys the current state of the study of tight surfaces. A geometric characterization of tightness is the following: a closed surface is tight if, and only if, every plane cuts the surface into at most two pieces. The first image shows an example of a tight surface: a torus of revolution. Here, a sample slicing plane cuts the surface into two parts, and it turns out that this is typical of any plane. The second image gives the canonical counter-example: there is a plane that cuts this surface into three pieces, so it is not tight. The article also included other computer-generated and hand-drawn images that I produced based on the descriptions given by Banchoff.

Davide P. Cervone's web pages Created: 08 Sep 2001 Last modified: Jan 6, 2002 10:37:20 PM Comments to: dpvc@union.edu

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