Inversions (Popular Lectures in Mathematics) - Softcover

Bakel'man, I. Ya. Ya.

 
9780226034997: Inversions (Popular Lectures in Mathematics)
Softcover
ISBN 10: 0226034992 ISBN 13: 9780226034997
Publisher: University of Chicago Press, 1975

Synopsis

In this book, I. Ya. Bakel'man introduces inversion transformations in the Euclidean plane and discusses the interrelationships among more general mathematical concepts. The author begins by defining and giving examples of the concept of a transformation in the Euclidean plane, and then explains the "point of infinity" and the "stereographic projection" of the sphere onto the plane. With this preparation, the student is capable of applying the theory of inversions to classical construction problems in the plane.

The author also discusses the theory of pencils of circles, and he uses the acquired techniques in a proof of Ptolemy's theorem. In the final chapter, the idea of a group is introduced with applications of group theory to geometry. The author demonstrates the group-theoretic basis for the distinction between Euclidean and Lobachevskian geometry.

"synopsis" may belong to another edition of this title.

From the Back Cover

In this book, I. Ya Bakel'man introduces inversion transformations in the Euclidean plane and discusses the interrelationships among more general mathematical concepts.

"About this title" may belong to another edition of this title.

Publisher
University of Chicago Press
Publication date
1975
Language
English
ISBN 10 
0226034992
ISBN 13 
9780226034997
Binding
Paperback
Number of pages
78