Teabag Problem (Was: Re: [math-fun] 3-D spider webs?)
Perhaps I should mention that the papery thing resembled two rectangles overlaid and joined along their perimeters. Which reminds me of the --------------------------------------------------------------------------------- TEABAG PROBLEM (which I learned of on the Web a few years ago): Let metric space T be 2 unit squares identified along their perimeter. Among all isometric embeddings of T in 3-space, what is the supremum of the attainable volumes? (And, is there an embedding that attains this sup? If so, which one(s)?) --------------------------------------------------------------------------------- It's even somewhat surprising that a positive volume is possible. --Dan _________________________________________________________________________ << 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.
On 10/7/07, Dan Asimov <dasimov@earthlink.net> wrote:
TEABAG PROBLEM (which I learned of on the Web a few years ago):
Let metric space T be 2 unit squares identified along their perimeter. Among all isometric embeddings of T in 3-space, what is the supremum of the attainable volumes?
1/8
(And, is there an embedding that attains this sup? If so, which one(s)?)
Tate & Lyle
It's even somewhat surprising that a positive volume is possible.
Not if one's misspent youth incorporated a splash course in origami water-bombs! But it must be admitted that I have no idea how to go about proving it ... WFL
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Dan Asimov -
Fred lunnon