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Inversions : Popular Lectures in Mathematics - J.W. Teller

Inversions

Popular Lectures in Mathematics

By: I.Y. Bakelman, I. Ya Bakel-Man, J.W. Teller (Translator), S. Williams (Translator)

Paperback Published: 1st January 1974
ISBN: 9780226034997
Number Of Pages: 82

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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.

ISBN: 9780226034997
ISBN-10: 0226034992
Series: Popular Lectures in Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 82
Published: 1st January 1974
Publisher: The University of Chicago Press
Country of Publication: US
Dimensions (cm): 23.0 x 15.4  x 0.64
Weight (kg): 0.11

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