# Bridges 2010 Short Paper

Playing with the Möbius Band

Eleonóra Stettner

(Proceedings pages 431–434)

## Abstract

If we are asked to visualize a Möbius band, we do not think first
of its symmetry. However, if we make a model of a Möbius band with
a computer program (for example, with Maple) and examine its boundary
from different points of view, we get various interesting, symmetrical
figures. A model of a Möbius band can be constructed by joining
the ends of a strip (long rectangle) of paper with a single half-twist.
It is interesting to observe how the resulting band transforms as
we vary the ratio between the long and short sides of the rectangle.
When will the surface intersect itself? We shall analyse these
problems with multiply-twisted strips. The second part of this
article deals with the connection between the Möbius band and
frieze patterns.

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