After (or before?) @StartsWithABang's balloon animals' post?A couple of week ago Ethan Siegel published a post about ballon animals, so I decide to repost an old piece that I wrote in 2011 for my italian blog: the english version is lost, but it is magically reposted here! I recently discovered this interesting site, vihart. In the site there are some interesting paper and today I want to write something about Computational Balloon Twisting: The Theory of Balloon Polyhedra by Erik and Martin Demaine and Vi Hart (the paper was reported in 2010 by the Improbable Research blog).
The interest about ballon twisting was motivated by...
Balloon twisting is fun: the activity can both entertain and engage children of all ages. Thus balloon twisting can be a vehicle for teaching mathematical concepts inherent in balloons. As we will see, these topics include graph theory, graph algorithms, Euler tours, Chinese postman tours, polyhedra (both 3D and 4D), coloring, symmetry, and even NP-completeness. Even the models alone are useful for education, e.g., in illustrating molecules in chemistry.There's also a second motivation: building architectural structures with air beams (Army blows up building, Center manages technology of inflatable composite structures).
Our approach suggests that one long, low-pressure tube enables the temporary construction of inflatable shelters, domes, and many other polyhedral structures, which can be later reconfigured into different shapes and re-used at different sites. In contrast to previous work, which designs a different inflatable shape specifically for each desired structure, we show the versatility of a single tube.The problem of the researchers is to determine the twistable graphs. Referring to a phisical balloon like a bloon, we have the following definitions:
(...) a bloon is a (line) segment which can be twisted at arbitrary points to form vertices at which the bloon can be bent like a hinge. The endpoints of a bloon are also vertices. Two vertices can be tied to form permanent point connections. A twisted bloon is stable if every vertex is either tied to another vertex or held at a nonzero bending angle.The three researchers also defined two models