Translation of W. Wunderlich’s “On a Developable Möbius Band”

“Explore, on a Mobius strip” offers an introduction to the mathematical subfield of topology by way of numerous hand-drawn sketches and an accessible discussion of going for a “walk” on a one-sided, one-edged Mobius strip—also known as a Mobius band. The chapter provides directions for making a Mobius strip out of paper and examining its mathematical properties. Mathematics students and enthusiasts are encouraged to explore more in both mathematics and life in order to expand their worldview. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

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Edge Majoranas on locally flat surfaces: The cone and the Möbius band

Physical Review B ◽

10.1103/physrevb.94.125137 ◽

2016 ◽

Vol 94 (12) ◽

Cited By ~ 10

Author(s):

A. Quelle ◽

C. Morais Smith ◽

T. Kvorning ◽

T. H. Hansson

Keyword(s):

Flat Surfaces ◽

Möbius Band

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The shape of a Möbius band

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1993.0009 ◽

1993 ◽

Vol 440 (1908) ◽

pp. 149-162 ◽

Cited By ~ 27

Keyword(s):

Aspect Ratio ◽

Asymptotic Solution ◽

Cross Section ◽

Rectangular Cross Section ◽

Elastic Rods ◽

Large Deflections ◽

Mechanical Equilibrium ◽

Elastic Rod ◽

Flexible Material ◽

Möbius Band

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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