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OverviewEuclidean and other geometries are distinguished by the transformations that preserve their essential properties. Using linear algebra and transformation groups, this book provides a readable exposition of how these classical geometries are both differentiated and connected. Following Cayley and Klein, the book builds on projective and inversive geometry to construct 'linear' and 'circular' geometries, including classical real metric spaces like Euclidean, hyperbolic, elliptic, and spherical, as well as their unitary counterparts. The first part of the book deals with the foundations and general properties of the various kinds of geometries. The latter part studies discrete-geometric structures and their symmetries in various spaces. Written for graduate students, the book includes numerous exercises and covers both classical results and new research in the field. An understanding of analytic geometry, linear algebra, and elementary group theory is assumed. Full Product DetailsAuthor: Norman W. Johnson (Wheaton College, Massachusetts)Publisher: Cambridge University Press Imprint: Cambridge University Press Dimensions: Width: 16.20cm , Height: 2.70cm , Length: 24.10cm Weight: 0.810kg ISBN: 9781107103405ISBN 10: 1107103401 Pages: 452 Publication Date: 07 June 2018 Audience: Professional and scholarly , College/higher education , Professional & Vocational , Tertiary & Higher Education Format: Hardback Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsReviewsAdvance praise: 'This extremely valuable book tells the story about classical geometries - euclidean, spherical, hyperbolic, elliptic, unitary, affine, projective - and how they all fit together. At the center are geometric transformation groups, both continuous groups such as isometry or collineation groups, and their discrete subgroups occurring as symmetry groups of polytopes, tessellations, or patterns, including reflection groups. I highly recommend the book!' Egon Schulte, Northeastern University, Massachusetts 'This extremely valuable book tells the story about classical geometries - euclidean, spherical, hyperbolic, elliptic, unitary, affine, projective - and how they all fit together. At the center are geometric transformation groups, both continuous groups such as isometry or collineation groups, and their discrete subgroups occurring as symmetry groups of polytopes, tessellations, or patterns, including reflection groups. I highly recommend the book!' Egon Schulte, Northeastern University, Massachusetts 'This is a book written with a passion for geometry, for complete lists, for consistent notation, for telling the history of a concept, and a passion to give an insight into a situation before going into the details.' Erich W. Ellers, zbMATH Author InformationNorman W. Johnson was Professor Emeritus of Mathematics at Wheaton College, Massachusetts. Johnson authored and co-authored numerous journal articles on geometry and algebra, and his 1966 paper 'Convex Polyhedra with Regular Faces' enumerated what have come to be called the Johnson solids. He was a frequent participant in international conferences and a member of the American Mathematical Society and the Mathematical Association of America. Tab Content 6Author Website:Countries AvailableAll regions |
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