Geometries and Transformations

Norman w. johnson (author)

350 pages, parution le 30/01/2018

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Résumé

Norman 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 �onvey 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.Introduction; 1. Homogenous spaces; 2. Linear geometries; 3. Circular geometries; 4. Real collineation groups; 5. Equiareal collineations; 6. Real isometry groups; 7. Complex spaces; 8. Complex collineation groups; 9. Circularities and concatenations; 10. Unitary isometry groups; 11. Finite symmetry groups; 12. Euclidean symmetry groups; 13. Hyperbolic coxeter groups; 14. Modular transformations; 15. Quaternionic modular groups.Euclidean 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.QA445Geometry.|Transformations (Mathematics)1EnglandCambridgeNorman W. Johnson.Advance 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

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Norman w. johnson (author)
Parution	30/01/2018
Nb. de pages	350
Format	156 x 234
Poids	810g
EAN13	9781107103405

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Geometries and Transformations

Résumé

Caractéristiques techniques

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