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Let’s Do the Twist

Topology is the study of the most fundamental characteristics of shape—the properties that are unaltered when bodies are stretched, twisted, or otherwise distorted. The London Underground map, originally devised by Harry Beck, is an everyday application of topology. Topology is often described as rubber-sheet geometry. Any two objects that can be transformed into each other by stretching, bending, and twisting are considered to be topologically equivalent as long as no tearing or gluing is required to transform one into the other. Chapter 21 explains topology by looking at some of the surfaces that can be formed by stretching and gluing the edges of a rectangle: the Möbius strip, the Klein bottle, and the torus.