Euclidean Geometry
Proof!: How the World Became Geometrical
Proof!
How the World Became Geometrical
Hardcover      ISBN: 0374254907
In this eye-opening narrative, an award-winning historian tells the monumental story of the geometrics that were carved into our world, the beliefs they supported and the ways they shape our lives to this day. Illustrations.
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.
Curves and Fractal Dimension
Curves and Fractal Dimension
Hardcover      ISBN: 0387940952
This book is written for mathematicians, engineers, researchers in experimental science, and anyone interested in fractals. It presents the fundamentals of curve analysis, including a new, clear introduction to fractal dimension, and requires only two years of calculus to understand the concepts. This text is appropriate for graduate study.
Curves and Fractal Dimension
Curves and Fractal Dimension
Paperback      ISBN: 1461286840
Written for mathematicians, engineers, and researchers in experimental science, as well as anyone interested in fractals, this book explains the geometrical and analytical properties of trajectories, aggregate contours, geographical coastlines, profiles of rough surfaces, and other curves of finite and fractal length. The approach is by way of precise definitions from which properties are deduced and applications and computational methods are derived. Written without the traditional heavy symbolism of mathematics texts, this book requires two years of calculus while also containing material appropriate for graduate coursework in curve analysis and/or fractal dimension.
Foundations of Convex Geometry
Foundations of Convex Geometry
Paperback      ISBN: 0521639700
This book presents the foundations of Euclidean geometry from the point of view of mathematics, taking advantage of all the developments since the appearance of Hilbert's classic work. Here, real affine space is characterized by a small number of axioms involving points and line segments making the treatment self-contained and thorough. This treatment is accessible for final year undergraduates and graduate students, and can also serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.
Geometry: Plane and Fancy
Geometry
Plane and Fancy
Hardcover      ISBN: 0387983066
GEOMETRY: Plane and Fancy offers students a fascinating tour through parts of geometry they are unlikely to see in the rest of their studies while, at the same time, anchoring their excursions to the well known parallel postulate of Euclid. The author shows how alternatives to Euclid's fifth postulate leads to interesting and different patterns and symmetries.
Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability
Geometry of Sets and Measures in Euclidean Spaces
Fractals and Rectifiability
Paperback      ISBN: 0521655951
The focus of this book is geometric properties of general sets and measures in Euclidean spaces. Applications of this theory include fractal-type objects, such as strange attractors for dynamical systems, and those fractals used as models in the sciences. The author provides a firm and unified foundation for the subject and develops all the main tools used in its study, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. The last third of the book is devoted to the Besicovitch-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of Euclidean space possessing many of the properties of smooth surfaces.
The King of Infinite Space: Euclid and His Elements
The King of Infinite Space
Euclid and His Elements
Paperback      ISBN: 0465065716
The Princeton University professor and best-selling author of Newton's Gift explores the origins and critical legacy of Euclid's influential book, The Elements, while demonstrating how scientists and thinkers throughout history have relied on his axiomatic system to shape human understandings of the world.
The Non-Euclidean Revolution
The Non-Euclidean Revolution
Paperback      ISBN: 0817647821
How unique and definitive is Euclidean geometry in describing the "real" space in which we live?Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world.Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world. A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America."Trudeau meets the challenge of reaching a broad audience in clever ways...(The book) is a good addition to our literature on non-Euclidean geometry and it is recommended for the undergraduate library."--Choice (review of 1st edition)"...the author, in this remarkable book, describes in an incomparable way the fascinating path taken by the geometry of the plane in its historical evolution from antiquity up to the discovery of non-Euclidean geometry. This 'non-Euclidean revolution', in all its aspects, is described very strikingly here...Many illustrations and some amusing sketches complement the very vividly written text."--Mathematical Reviews