# Möbius strip unravelled

From Nature:

Eugene Starostin’s desk is littered with rectangular pieces of paper. He picks one up, twists it, and joins the two ends with a pin. The resulting shape has a beautiful simplicity to it — the mathematical symbol for infinity in three-dimensional form. “Look,” he says, as he traces his finger along its side, “whatever path you take, you always end up where you started.” Discovered independently by two German mathematicians in 1858 — but named after just one of them — the Möbius strip has beguiled artists, illuminated science lessons and stubbornly resisted definition.

Until now, that is. Starostin and his colleague Gert van der Heijden, both of University College London, have solved a conundrum that has perplexed mathematicians for more than 75 years — how to predict what three-dimensional form a Möbius strip will take. The strip is made from what mathematicians call a ‘developable’ surface, which means it can be flattened without deforming its shape — unlike, say, a sphere. When a developable surface is formed into a Möbius strip, it tries to return to a state of minimum stored elastic energy, like an elastic band springing back after being stretched. But no one has been able to model what this final form will be. “The first papers looking at this problem were published in 1930,” says Starostin. “It seems such a simple question — children can make these things — but ask the experts how to model this shape and we’ve had nothing.”

More here.