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About this product
- DescriptionCircles and spheres are central objects in geometry. Mappings that take circles to circles or spheres to spheres have special roles in metric and conformal geometry. An example of this is Lie's sphere geometry, whose group of transformations is precisely the conformal group. Coolidge's treatise looks at systems of circles and spheres and the geometry and groups associated to them. It was written (1916) at a time when Lie's ermous influence on the field was still widely felt. Today, there is a renewed interest in the geometry of special geometric configurations. Coolidge has examined many of the most intuitive: linear systems of circles, circles orthogonal to a given sphere, and so on. He also examines the differential and projective geometry of the space of all spheres in a given space.Through the simple vehicles of circles and spheres, Coolidge makes contact with diverse areas of mathematics: conformal transformations and analytic functions, projective and contact geometry, and Lie's theory of continuous groups, to name a few. The interested reader will be well rewarded by a study of this remarkable book.
- Author(s)Julian Lowell Coolidge
- PublisherAmerican Mathematical Society
- Date of Publication13/12/2004
- Series TitleAMS Chelsea Publishing
- Series Part/Volume Number236
- Place of PublicationProvidence
- Country of PublicationUnited States
- ImprintAmerican Mathematical Society
- Weight1106 g
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