Inversions
I.Y. Bakelman(Author)
University of Chicago Press
Published on 15. February 1975
Book
Paperback/Softback
77 pages
978-0-226-03499-7 (ISBN)
Description
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.
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.
More details
Series
Language
English
Place of publication
Chicago
United States
Publishing group
The University of Chicago Press
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 23 mm
Width: 15 mm
Thickness: 1 mm
Weight
142 gr
ISBN-13
978-0-226-03499-7 (9780226034997)
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Schweitzer Classification