bellows conjecture

Akordeonbalg.jpg

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.

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