Foundations of Geometry
Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace
Euclid's Window
The Story of Geometry from Parallel Lines to Hyperspace
Paperback      ISBN: 0684865246
The history of geometry in relation to "space" discusses the contributions of Pythagoras, the advent of Albert Einstein's "fourth dimension," and the discovery of seven more dimensions by Princeton mathematician Edward Witten.
Philosophical Geometry
Philosophical Geometry
Paperback      ISBN: 0892811161
Ancient Egyptians and Greeks (up to Euclid) saw in plane geometry much more than land-surveying. For the Greeks, Gaia or Ge (from which our word “geometry
Aristotle on God's Life-Generating Power and on Pneuma as Its Vehicle
Aristotle on God's Life-Generating Power and on Pneuma as Its Vehicle
Hardcover      ISBN: 1438468296
Proposes an innovative rethinking of Aristotle
Curved Spaces: From Classical Geometries to Elementary Differential Geometry
Curved Spaces
From Classical Geometries to Elementary Differential Geometry
1st Edition    Paperback      ISBN: 0521713900
This self-contained textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra.
Curved Spaces: From Classical Geometries to Elementary Differential Geometry
Curved Spaces
From Classical Geometries to Elementary Differential Geometry
1st Edition    Hardcover      ISBN: 0521886295
This self-contained textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra.
Foundations of Geometry and the Non-Euclidean Plane
Foundations of Geometry and the Non-Euclidean Plane
Hardcover      ISBN: 0387906940
Mathematics Mechanization and Applications
Mathematics Mechanization and Applications
Hardcover      ISBN: 0127347607