From cube-lovers-errors@mc.lcs.mit.edu Wed Apr 22 14:41:52 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id OAA01093; Wed, 22 Apr 1998 14:41:51 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Wed Apr 22 14:20:19 1998 Date: Wed, 22 Apr 1998 14:24:21 -0400 (Eastern Daylight Time) From: Jerry Bryan Subject: Re: Hamiltonian circuits on the cube In-Reply-To: <9804221542.AA10123@sun28.aic.nrl.navy.mil> To: Dan Hoey Cc: whuang@ugcs.caltech.edu, cube-lovers@ai.mit.edu Message-Id: On Wed, 22 Apr 1998, Dan Hoey wrote: > whuang@ugcs.caltech.edu (Wei-Hwa Huang) writes: > > > I was pretty surprised to come up with this within ten minutes of reading > > the question: > > Wow, I'm impressed. I thought I'd have to write a program to find > them, and here's a nice symmetric solution. The symmetry is more > visible in a different unfolding: > Not to minimize the difficulty of the problem or the beauty of the solution (quite the contrary), but the solution seems almost trivial when viewed in the light of Dan's particular unfolding of the surface of the cube. The same comment is true of Dan's isoglyphic solution. It makes me wonder of you actually saw Dan's unfolding in your mind's eye, as it were, as you worked out your solution. Or another way to put it, did you work out your solution in 2-D or in 3-D? It also makes me wonder if there is any other unfolding that would lead as naturally to a Hamiltonian circuit. I tend to think not, but I could well be wrong. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990