From - Sat Apr 25 17:14:38 1998
From: Jeff Erickson
Newsgroups: sci.math
Subject: Re: Volume of a "feed sack"
Date: Fri, 24 Apr 1998 17:46:11 -0400
Organization: Center for Geometric Computing, Duke University
Alan Androski wrote:
> A colleague of mine was recently asked by a farmer if there might be
> some formula for the volume of a feed sack.
This sounds like Paul Earwicker's "tea-bag problem" -- How much volume
can you enclose in a tea-bag formed by gluing together the boundaries of
two unit squares of paper, with no stretching or tearing allowed?
The exact answer is unknown, but it's between 0.2055 and 0.2176. [An
easy lower bound of 0.125 is given by a 1/2 by 1/2 by 1/2 cube with some
triangular flaps, which is easy to fold. An easy upper bound of 0.266
is given by the volume of a sphere with surface area 2.]
See "http://www.ics.uci.edu/~eppstein/junkyard/teabag.html" for some
older results and the original source of the tea-bag problem, and
"http://frey.newcastle.edu.au/~andrew/teabag/" for the most recent (and
extremely cool) results, which are due to Andrew Kepert.
--
Jeff Erickson Center for Geometric Computing
jeffe@cs.duke.edu Department of Computer Science
http://www.cs.duke.edu/~jeffe Duke University
References:
- http://compgeoms.cs.uiuc.edu/~jeffe/open/open.html