A simpler $\mathbb R^3$ realization of the M\"obius strip

TL;DR

This paper presents a new, simpler $\

Contribution

It introduces a more straightforward $\

Findings

The realization is the union of a vertical segment and a graph of a rational function.

It works for any width/length ratio of the M"obius strip.

The new realization is significantly simpler than the common one.

Abstract

A very simple $\mathbb R^3$ realization of the M\"obius strip, significantly simpler than the common one, is given. For any, however large width/length ratio of the strip, it is shown that this realization, in contrast with the common one, is the union of a vertical segment and the graph of a simple rational function on a simple polynomially defined subset of $\mathbb R^2$.