Since 1930, the Moebius strip has been a classic poser for experts in mechanics. The teaser is to resolve the strip algebraically–to explain its unusual shape in the form of an equation.
In a study published on Sunday that lyrically praises the strip for its “mathematical beauty,” two experts in non-linear dynamics, Gert van der Heijden and Eugene Starostin of University College London, present the solution.
What determines the strip’s shape is its differing areas of “energy density,” they say.
“Energy density” means the stored, elastic energy that is contained in the strip as a result of the folding. Places where the strip is most bent have the highest energy density; conversely, places that are flat and unstressed by a fold have the least energy density.