Study of cutting the Möbius

Ekaterina Y. Arutyunova

Vol. 1, Issue 2, p 26-29 (2019)

Download the Article Here

ABSTRACT: The paradox of cutting the Möbius strip is that longitudinal cutting is ambiguous, unlike a cylindrical surface. The configurations and geometrical dimensions of the obtained strips depend on the distance from the cut to the edge of the surface. For example, if there was cutting into one-sixth of the width of a cylindrical surface, it will result in two separate cylindrical surfaces of different widths. This is different with a Möbius strip: if there was cutting into one-sixth of the width of a Möbius surface, it produces two connected strips. One of the strips is twice as large as the original Möbius strip and has 3 twists, and the second one is the same as initial Möbius strip. To date, the parameters and characteristics of the Möbius strip have been reliably identified, which determine the ambiguity of the cutting result, unlike a cylindrical surface.
The interest in the cutting paradox is of both scientific and of practical interest for cardiac surgery. If we manage to resolve this paradox, that is, to find out what parameters and characteristics lead to the ambiguity of the cutting, this will solve one of the problems in cardiac surgery.
Thus, the problem (of which the solution is described in this article) is the identification, experimentally and theoretically, of factors that determine the uniqueness of the configurations obtained by cutting a Möbius strip and studying the resulting configurations
KEYWORDS: Topology; Cylindrical surface; Möbius Strip; One-sided Surface; Surface cutting