Discussion:  All Topics in Geometry 
Topic:  Physical models of surfaces 
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Subject:  RE: Physical models of surfaces 
Author:  gerirose 
Date:  Jan 23 2008 
"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 AprilMay and then JuneAugust in
Hayward Gallery in London  they requested my newest piece as intro  I just
posted photos of it here:
http://www.flickr.com/photos/21541981 @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, NonEuclid, 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
Scott Steketee
> Sketchpad Projects
 
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