The shape of a Möbius band
L. Mahadevan, Joseph Bishop Keller
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Source: Crossref
Published: Jan 8, 1993
DOI: 10.1098/rspa.1993.0009
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Abstract 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.
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