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Topic: Physical models of surfaces

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Subject:   RE: Physical models of surfaces
Author: stek
Date: Jan 22 2008
Hi Peter,

On Jan 22 2008, Peter Ash wrote:
> 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.

The most effective physical model I've seen is the crochet hyperbolic plane
invented by Daina Taimina from Cornell. It has a uniform curvature throughout,
and you can investigate all kinds of geometric questions using it. However, I
don't know if anyone is making these yet for sale, so you might have to learn a
new skill! There's lots of information on the web; just do a search for "crochet
hyperbolic geometry." You'll get plenty of hits, with lots of good info.

As far as software goes, Non-Euclid, from Joel Castellanos (at University of
New Mexico) and several collaborators, is designed for just such investigations.
It uses the Poincare disk model. Alternatively, if you already have The
Geometer's Sketchpad, look in the Samples | Sketches | Investigations folder for
Poincare Disk.gsp, which provides an extensive set of custom tools for
hyperbolic constructions.

Good luck,

Scott Steketee
Sketchpad Projects

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