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 Alfred North Whitehead - Cambridge University Press
In this book, after the statement of the axioms, the ideas considered are those concerning the association of Projective and Descriptive Geometry by means of ideal points, point to point correspondence, congruence, distance, and metrical geometry.
by Conway, Doyle, Thurston - Rutgers University, Newark
These are notes from an experimental mathematics course entitled Geometry and the Imagination as developed by Conway, Doyle, Thurston and others. The course aims to convey the richness, diversity, connectedness, depth and pleasure of mathematics.
by Derrick Norman Lehmer - Project Gutenberg
The book gives, in a simple way, the essentials of synthetic projective geometry. Enough examples have been provided to give the student a clear grasp of the theory. The student should have a thorough grounding in ordinary elementary geometry.
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.