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The shape of a Möbius band. (English) Zbl 0786.73041

Summary: The shape of a Möbius band made of a flexible material, such as paper, is determined. The band is represented as a bent, twisted elastic rod with a rectangular cross-section. Its mechanical equilibrium is governed by the Kirchhoff-Love equations for the large deflections of elastic rods. These are solved numerically for various values of the aspect ratio of the cross-section, and an asymptotic solution is found for large values of this ratio. The resulting shape is shown to agree well with that of a band made from a strip of plastic.

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74B20 Nonlinear elasticity
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