I have only just worked out (I think) what was meant by "swim through itself" here, reminding me of this animation of a 7-link rotating smoke-ring robot with just one nontrivial degree of freedom, which I don't recall having mentioned on math-fun before: https://www.dropbox.com/s/aeo6rxtc5j4p291/sevenring.gif Open in a browser for the animation to execute: it should do so in situ, with no need to downoad first. Fred Lunnon On 5/28/14, Dan Asimov <dasimov@earthlink.net> wrote:
The Bellows Theorem* (formerly Conjecture) states that for any closed, triangulated polyhedron in 3-space that flexes, its volume remains constant. This would impose severe constraints on a circular concertina (its polyhedron could always be triangulated), but maybe it's possible.
--Dan
_________________________________________________________________ * http://www.emis.ams.org/journals/BAG/vol.38/no.1/b38h1csw.ps.gz
On May 28, 2014, at 11:37 AM, Allan Wechsler <acwacw@gmail.com> wrote:
There are many tube-like accordion folds. If any of them permit any bending, they could be bent into a ring that would almost certainly permit the toroidal rotation that Jim remembers from that cubical toy. (I think we may have one.)
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun