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