28 May
2014
28 May
'14
1:27 p.m.
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.)