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

  • Russell E. TodresEmail author


The following is a translation of Walter Wunderlich’s article “Über ein abwickelbares Möbiusband”, which appeared in the Monatshefte für Mathematik66 (1962), 276–289 and was dedicated to Prof. Dr. Paul Funk on the occasion of his 75th birthday. Wunderlich summarizes Sadowsky’s work (Sitzber. Preuss. Akad. Wiss. 22:412–415, 1930; Verhandlungen des 3. Internationalen Kongresses für Technische Mechanik, II (Stockholm, 1930), pp. 444–451, Sveriges Litografiska Tryckerier, Stockholm, 1931) on developable Möbius bands and improves Sadowsky’s upper bound of the dimensionally-reduced variational description for determining the configuration of a Möbius band whose width is small in comparison to its length. Attempting to reproduce the equilibrium depiction of a band of finite width, using a rational-algebraic developable, Wunderlich then extends Sadowsky’s results by presenting perhaps the first successful model of a closed, analytic, developable Möbius band with associated thinness bounds. This translation makes Wunderlich’s work accessible to the broader research community at a time of growing interest in and relevance of thin-walled structural elements.


Möbius bands Differential geometry Developable surfaces 

Mathematics Subject Classification

53A04 74G10 74G55 74K10 74K20 01A75 


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Mathematical Soft Matter UnitOkinawa Institute of Science and TechnologyOkinawaJapan

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