## bellows conjecture

image source wikipedia: unfinished Accordion bellows

A remarkable mathematical conjecture (proven 1995 by Sabitov) is that there exists no rigid bellows. This means if you have a closed volume which is formed by (triangle shaped) “plates” and if you deform it then the volume stays always constant (i.e. if it would have been a bellows then you couldnt press air out of it). This is why accordions need some elastic fabric in order to allow for deformation. May be also a useful knowledge for architecture, since it means that if you press a (closed) house on one side it would bulb on some other side.

The workshop Rigidity and polyhedral combinatorics is discussing related problems.

### 2 Responses to “bellows conjecture”

1. KRESLING, Biruta Says:

Nov. 25, 2018
Ms. Biruta KRESLING (German architect, designer and scientist living in Paris:
In 1992 a student of mine at the ARTS DECORATIFS in Paris found a pattern that is obtained by “twist buckling”. During 16 years I improved the pattern, and am able now to provoke the pattern spontaneously (at least three modes: 1,2,3…) in less one second.

I discoverd that this nearly stress free folding pattern exists in the “bellows” of Achaerontia atropos”, a giant hawkmoth that visits bee hives, even in Britain (!) – thanks to L.T. Wasserthal (German zoologist).
The pattern is named after me “Kresling Pattern” – “Kresling origami”- “Kresling Tower” and so on.
See: Biruta Kresling: Natural twist buckling in shells: from the hawkmoth’s bellows to the deployable “Kresling-pattern” and cylindrical “Miura-ori” (published in 2008)
A first technological application is proposed by Wilson, Pellegrino et al.(CALTECH, Pasadena and Northrop Gumman) for a foldable sunshield of the IXO Space Telescop, to be launched in 2028 (?)
See:Wilson, L., Pellegrino, S. and Danner, R. (2013), Origami inspired concepts for space telescopes, 54nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 9 April 2013, Boston, MA,

Since 2008 at least 30 applications and research topics are based upon the “Kresling Pattern”
Best regards Biruta Kresling

you can use LaTeX in your math comments, by using the $shortcode: [latex] E = m c^2$