Comment on Y.-C. Chen, E. Fried, Möbius bands,
unstretchable material sheets and developable surfaces.
Proc. R. Soc. A 472, 20160459 (2016)
G.H.M. van der Heijden & E.L. Starostin
Chen & Fried claim that our solution of the shape of a material Möbius
strip (taken to be inextensible) in Nature Materials 6 (2007)
is incorrect as it involves stretching of the material. The purported proof
of this claim, the calculation in §7, is in fact the main result of the
paper. The claim is elaborated upon in subsequent publications with Fosdick.
Here, we show that all these papers are based on a misunderstanding of the
elastic deformation involved and what it means for such a deformation to be
isometric (i.e. to preserve distances).
keywords: elastic strip, isometric deformation, developable surface
Proc. R. Soc. A 478, 20210629 (2022)