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: 15

Answer

The genus of a pitcher is two.

Work Step by Step

In topology, the objects are classified by the genus of the object, 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 pitcher, we can see that the largest number of complete cuts that can be made in the object without cutting it into two pieces is two. So, the genus of the given object is two. Hence, the genus of the given object is two.
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