most recent 30 from http://mathoverflow.net 2013-05-21T10:42:48Z http://mathoverflow.net/feeds/question/29591 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/29591/sticks-and-thread Pietro Majer 2010-06-26T08:40:14Z 2010-07-01T18:26:01Z

<p>In this recent question <a href="http://mathoverflow.net/questions/29323/math-puzzles-for-dinner/29343#29343" rel="nofollow">http://mathoverflow.net/questions/29323/math-puzzles-for-dinner/29343#29343</a> we had a nice time as we were asked to provide new maths puzzles for dinners. I suggested the following:</p> <blockquote> <p>Given three equal sticks, and some thread, is it possible to make a rigid object in such a way that the three sticks do not touch each other? (all objects are 1 dimensional; sticks are straight and rigid, and the thread is inestensible).</p> </blockquote> <p>I'm not particularly fond of maths puzzles, and I found this one in order to satisfy the party in a dinner of non-mathematic people, when I'm asked for a puzzle. Indeed, it's suitable for a dinner, and people get to the right conclusion in reasonable time, amusing themselves and disputing a bit. </p> <p>Possibly as a consequence of the fact that I always proposed it to non-mathematicians, who are not interested in the proof, now I realized that I do not have, or I forget, the proof for the answer (a bit embarassing indeed). Can somebody find a quick proof for the answer, without too many technical computations?</p>

http://mathoverflow.net/questions/29591/sticks-and-thread/29599#29599 Steve Huntsman 2010-06-26T12:02:12Z 2010-06-26T12:02:12Z

<p>Instead of a proof, I will provide references. It's called a "tensegrity prism". See especially sections 1.4, 3.5 and 3.6 of <a href="http://books.google.com/books?id=LxItccmYhBkC" rel="nofollow"><em>Dynamics and Control of Tensegrity Systems</em></a>. Also see <a href="http://www-civ.eng.cam.ac.uk/dsl/publications/tensegrity.pdf" rel="nofollow">"Review of Form-Finding Methods for Tensegrity Structures"</a> and the MS thesis <a href="http://scholar.lib.vt.edu/theses/available/etd-12022002-155829/" rel="nofollow"><em>Kinematic Analysis of Tensegrity Structures</em></a>.</p>