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Inversions (Popular Lectures In Mathematics) | I. Ya. Bakel’man

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Inversions (Popular Lectures In Mathematics)
Original Title Inversions (Popular Lectures In Mathematics)
Author I. Ya. Bakel’man
Publication date

Topics mathematics, circles, geometry, ptolemy’s theorem, groups, euclidean geometry, lobachevskian geometry, sterorgraphic projections, sphere, transformations
Collection mir-titles, additional_collections
Book Type EBook
Material Type Book
File Type PDF
Downloadable Yes
Support Mobile, Desktop, Tablet
Scan Quality: Best No watermark
PDF Quality: Good
Availability Yes
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n this book, I. Ya. Bakel’man introduces inversion trans­ formations 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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