Re: Teabag Problem (Was: Re: [math-fun] 3-D spider webs?)
It's even somewhat surprising that a positive volume is possible.
--Dan
It surprised me until I found an origami example on the internet. There's whole lot of stuff on this problem, e.g. http://www.ics.uci.edu/~eppstein/junkyard/teabag.html but I couldn't find anything on the natural question, what if instead of a square you have a disc? Can there be a positive volume? dg
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<< Jim asks:
<< Do any spiders build genuinely three-dimensional webs?
Just Friday I turned over an 8-inch rock from our garden0, and clinging to the bottom were two thin earthworms and a paperish thing that resembled the remains of some kind of cocoon. When that thing started flexing, I thought we were about to witness the emergence of some insect's next stage. But instead -- after about five minutes of flexing -- out walked a spider -- a black one quite fat (probably expecting) -- looking quite formidable.
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David Gale Professor Emeritus Department of Mathematics University of California, Berkeley
On 10/10/07, David Gale <gale@math.berkeley.edu> wrote:
... It surprised me until I found an origami example on the internet. There's whole lot of stuff on this problem, e.g. http://www.ics.uci.edu/~eppstein/junkyard/teabag.html
One of the most detailed accounts near the end of this page, signed Narasimham G.L., mysteriously peters out in the middle (quite literally!). But it seems from that and other contributions that the optimal solution does not actually have the symmetry of the square --- which I find highly counter-intuitive. Another point that nobody seemed to pick up about the early attempts at solution (such as my casually suggested 1/8 cube) is that any flat flap results in an immersion rather than a proper embedding; but that carp was in any case overtaken by later events. Fascinating material about a beautiful problem! WFL
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David Gale -
Fred lunnon