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OverviewAffine, projective, spherical, Möbius, and hyperbolic geometries are covered by this textbook. Special emphasis is given on the groups of transformations in the spirit of the Erlangen program of Felix Klein as transformation groups not only provide a theoretical basis for the geometries, but also allow to solve concrete problems, which are an organic part of the book. By establishing direct connections and by looking at the same notion or problem from different points of view the author gives a harmonic overview of the geometry. Starting with classical topics such as conics and quadrics, duality and polarity, cross-ratio, spherical and hyperbolic trigonometry he leads to less classical ones like compositions of reflections, volumes of spherical and hyperbolic tetrahedra, billiards, de Sitter geometry. As only the knowledge of linear algebra, complex numbers and basic group theory is required this book is accessible to second year undergraduate students. However, graduate students in algebraic geometry, differential geometry, or geometric topology will also find this basic inventory of what every geometer should know a helpful hand. Full Product DetailsAuthor: Ivan IzmestievPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2021 ISBN: 9783319503691ISBN 10: 3319503693 Publication Date: 21 June 2021 Audience: College/higher education , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: Not yet available This item is yet to be released. You can pre-order this item and we will dispatch it to you upon its release. Table of ContentsReviewsAuthor InformationIvan Izmestiev is a professor at University of Fribourg Tab Content 6Author Website:Countries AvailableAll regions |