* Thane Plambeck <thane@best.com> [Feb 25. 2006 06:28]:
This is from Courant and Robbins, "What is Mathematics", pg 214
* * * One of the most remarkable properties of the hyperboloid is that although it contains two families of intersecting straight lines, these lines do not make the surface rigid. If a model of the surface is constructed from wire rods, free to rotate at each intersection, then the whole figure may be continuously deformed into a variety of shapes
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So, I'd like to play with such a model. Can I buy one somewhere? Does anything come to mind? I doubt I have patience to make one. I'm also a bit unclear on what "free to rotate at each intersection" means in the quoted passage. Can you fold it into nonhyperboloids?
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Wild guess (please confirm): degree of freedom is same as if connecting two rings with threads and twist them. 0 degree ==> cylinder 180 degree ==> two facing cones everything in between: hyperboloid. That how I visualized hyperboloids on the good old apple2. Was I correct? -- p=2^q-1 prime <== q>2, cosh(2^(q-2)*log(2+sqrt(3)))%p=0 Life is hard and then you die.