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Topic: Physical models of surfaces

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Subject:   RE: Physical models of surfaces
Author: gerirose
Date: Jan 23 2008
Here's a response from Daina Tamina:

"Thank you for a nice reference to crocheted hyperbolic planes! They now have
their own life :-)
If you are on the list who had this discussion, you can mention that in
wikipedia they can search for hyperbolic soccer ball - that is paper model, all
instructions posted by David's son Keith how he was making hyperbolic planes
from paper with his students.

On a note about hyperbolic crochet planes - as you might have heard there is a
huge project going on - Crocheted Coral Reef - they call me Original Creator.
Coral Reef will be on exhibit in NYC April-May and then June-August in
Hayward Gallery in London - they requested my newest piece as intro - I just
posted photos of it here: @N02/"

On Jan 22 2008, stek wrote:
> 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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