RUBBER BANDS, BASEBALLS AND DONUTS: A Book About Topology

There are more abstract and unfamiliar concepts introduced here than in most of the Young Math books, and this is also more textbookish in its emphasis on terminology and classification. However Froman does an expert job of giving intuitive clarity to the basics of topology, beginning with a stretched rubber band and a line segment drawn on crumpled paper to illustrate the concept of variants and invariants (""the things that do not change"" with distortion). A look at the properties of simple closed curves leads to a classification of objects into genus 0, 1, 2, 3, etc., according to ""how many times you can cut through it and still leave it in one piece,"" and a demonstration (with a phonograph record, donut, and teacup, all genus 1) of how any object in a particular genus ""can be changed into (another) without any cutting or tearing. The pictures, which include a group of cartoony birds as commenting stand-ins for the reader, help make all this mind stretching painless and even entertaining.