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Topic: Physical models of surfaces

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Subject:   Physical models of surfaces
Author: Peter Ash
Date: Jan 22 2008
I would like to obtain an actual physical model of a surface exhibiting negative
curvature. The purpose is to have my students (who are high school teachers)
discover that the sum of the angles in a triangle on such a surface will be less
than 180 degrees by (1) constructing the triangles using pushpins and rubber
bands and then (2) figuring out how to (roughly) measure the angles formed.

If software is available to simulate this, I'd like to know, but I feel that
manipulating actual objects is more valuable than working with virtual objects.
The surface I'd like to have could be the classical saddle surface, a
pseudosphere, or even a torus. Perhaps there are some found objects I could use
(a bagel? a toy saddle?). Or does anyone know of a website where one could enter
a surface description and receive a physical (cardboard?) model using 3-D
printing techniques? I don't want to spend more than $100 and would like to make
10 models.

Any ideas?

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