Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.7 Beyond Euclidean Geometry - Exercise Set 10.7 - Page 676: 16

Answer

The genus of a wrench is two.

Work Step by Step

Topology is a modern branch of geometry in which shapes, unlike Euclidean geometry, are not rigid. In topology, shapes can be twisted, bent or stretched to form another shape. The objects are classified by the genus, which is the number of holes in the object. It can also be said that the number of cuts that can be made in that object without rendering that object into two pieces is known as its genus. In the given figure of a wrench, we can see that the number of cuts that can be made in the object without rendering the object into two pieces is two.
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