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The present introduction deals with the metrical and to a slighter extent with the projective aspect. A third aspect, which has attracted much attention recently, from its application to relativity, is the differential aspect. This is altogether excluded from the present book. In this book a complete systematic treatise has not been attempted but have rather selected certain representative topics which not only illustrate the extensions of theorems of hree-dimensional geometry, but reveal results which are unexpected and where analogy would be a faithless guide. The first four chapters explain the fundamental ideas of incidence, parallelism, perpendicularity, and angles between linear spaces. Chapters V and VI are analytical, the former projective, the latter largely metrical. In the former are given some of the simplest ideas relating to algebraic varieties, and a more detailed account of quadrics, especially with reference to their linear spaces. The remaining chapters deal with polytopes, and contain, especially in Chapter IX, some of the elementary ideas in analysis situs. Chapter VIII treats hyperspatial figures, and the final chapter establishes the regular polytopes.
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- PublisherDover
- Publication date1958
- ISBN 10 0486604942
- ISBN 13 9780486604947
- BindingPaperback
- Edition number1
- Number of pages196
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An Introduction to the Geometry of N Dimensions
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Book Description Paperback. Condition: Fair. No Jacket. Readable copy. Pages may have considerable notes/highlighting. ~ ThriftBooks: Read More, Spend Less 0.55. Seller Inventory # G0486604942I5N00
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Book Description Paperback. Condition: Good. No Jacket. Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less 0.55. Seller Inventory # G0486604942I3N00
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Book Description Paperback. Condition: Very Good. Softcover. Good binding and cover. Shelf wear. Edge rubbed. Owner's name on edge and end page. In the first four chapters, author D. M. Y. Sommerville explains the fundamental ideas of incidence, parallelism, perpendicularity, and angles between linear spaces. Chapter V presents analytical geometry from the projective point of view, exploring some of the simplest ideas relating to algebraic varieties and offering a more detailed account of quadratics. Chapter VI examines analytic geometry of n dimensions from the metric point of view. The remaining four chapters deal with polytopes and address some of the elementary ideas in analysis situs. Chapter VIII treats the content of hyper-special figures, and the final chapter establishes the regular polytope. Seller Inventory # 2404100017
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