Translation of Michael Sadowsky's paper "An elementary proof for the existence of a developable M\"obius band and the attribution of the geometric problem to a variational problem"

TL;DR

This paper translates Sadowsky's 1930 work demonstrating the existence of a developable Möbius band and reformulating the geometric problem as a variational problem, providing foundational insights into the mathematical properties of such structures.

Contribution

It provides the first English translation of Sadowsky's original proof and highlights the connection between the geometric problem and variational methods.

Findings

Existence proof of a developable Möbius band.

Reduction of the geometric problem to a variational problem.

Historical significance of Sadowsky's approach.

Abstract

This article is a translation of Michael Sadowsky's original paper "Ein elementarer Beweis f\"ur die Existenz eines abwickelbaren M\"obiusschen Bandes und die Zur\"uckf\"uhrung des geometrischen Problems auf ein Variationsproblem." which appeared in Sitzungsberichte der Preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, 17. Juli 1930, Mitteilung vom 26. Juni, 412-415. Published on September 12, 1930.