The Geometry of the Sphere
by John C. Polking
Publisher: Rice University 2000
We are interested here in the geometry of an ordinary sphere. In plane geometry we study points, lines, triangles, polygons, etc. On the sphere we have points, but there are no straight lines. Therefore it is natural to use great circles as replacements for lines. Then we can talk about triangles and polygons and other geometrical objects.
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by Sigurdur Helgason - Birkhauser Boston
The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications.
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This volume includes articles exploring geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension.
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The present book grew out of notes written for a course by the same name taught by the author during in 2005. Only some basic abstract algebra, linear algebra, and mathematical maturity are the prerequisites for reading this book.
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A continually updated book devoted to rigorous axiomatic exposition of the basic concepts of geometry. Self-contained comprehensive treatment with detailed proofs should make this book both accessible and useful to a wide audience of geometry lovers.