The shape of a Möbius band
- 8 January 1993
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
- Vol. 440 (1908) , 149-162
- https://doi.org/10.1098/rspa.1993.0009
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.Keywords
This publication has 3 references indexed in Scilit:
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- Collocation Software for Boundary-Value ODEsACM Transactions on Mathematical Software, 1981
- ber ein abwickelbares M biusbandMonatshefte für Mathematik, 1962