Geometries / A.B. Sossinsky.

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The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to...

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Bibliographic Details
Main Author: Sosinskiĭ, A. B. (Alekseĭ Bronislavovich)
Language:English
Published: Providence, R.I. : American Mathematical Society, [2012], ©2012.
Series:Student mathematical library ; v. 64.
Subjects:
Geometry > Textbooks.
Geometry.
Geometry > Instructional exposition (textbooks, tutorial papers, etc.)
Geometry > Research exposition (monographs, survey articles)
History and biography > History of mathematics and mathematicians > Greek, Roman.
History and biography > History of mathematics and mathematicians > 19th century.
Category theory; homological algebra > Instructional exposition (textbooks, tutorial papers, etc.)
Textbooks.
Genre:
Textbooks.
Physical Description:xvi, 301 pages : illustrations ; 22 cm.
Format: Book
Contents:
  • About Euclidean geometry
  • Toy geometries and main definitions
  • Abstract groups and group presentations
  • Finite subgroups of SO(3)
  • Discrete subgroups of the isometry group of the plane and tilings
  • Reflection groups and Coxeter geometries
  • Spherical geometry
  • The Poincaré disk model of hyperbolic geometry
  • The Poincaré half-plane model
  • The Cayley-Klein model
  • Hyperbolic trigonometry and absolute constants
  • History of non-Euclidean geometry
  • Projective geometry
  • "Projective geometry is all geometry"
  • Finite geometries
  • The hierarchy of geometries
  • Morphisms of geometries
  • Excerpts from Euclid's "Elements"
  • Hilbert's axioms for plane geometry.