ENGLISH

Inversions

By I. Ya. Bakel'man , Joan W. Teller , Susan Williams

Book information

Publisher
University of Chicago Press
Year
1974
ISBN
0226034992, 9780226034997
LCC
QA473 .B3413
Open Library ID
OL5045557M
Language
english
Format
DJVU
Filesize
645 kB (660397 bytes)
Series
Popular lectures in mathematics
Pages
78\78
Topic
Education
Library
Kolxo3
DPI
600
Scanned
yes
Time added
2009-07-20 03:45:11

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.>

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