Inversions
Book Details
Format
Paperback / Softback
Book Series
Popular Lectures in Mathematics PLM
ISBN-10
0226034992
ISBN-13
9780226034997
Publisher
The University of Chicago Press
Imprint
University of Chicago Press
Country of Manufacture
US
Country of Publication
GB
Publication Date
Feb 15th, 1975
Print length
77 Pages
Weight
148 grams
Dimensions
23.00 x 15.30 x 0.60 cms
Ksh 4,300.00
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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.
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