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Euclidean & Non-Euclidean Geometries: Development and History
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Marvin J Greenberg
This book presents the discovery of non-Euclidean geometry and the subsequent reformulation of the foundations of Euclidean geometry. The book provides a selection of topics suitable for the undergraduate student. A feature of this text is that some new results are developed in the exercises and then built upon in subsequent chapters. Many new ...
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Geometry, Relativity and the Fourth Dimension
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Rudy Von B Rucker
Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.
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A Gateway to Modern Geometry: The Poincare Half-Plane
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Saul Stahl
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Taxicab Geometry: An Adventure in Non-Euclidean Geometry
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Eugene Krause
Develops a simple non-Euclidean geometry and explores some of its practical applications through graphs, research problems, and exercises. Includes selected answers.
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Convex polytopes
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Branko Grünbaum
The appearance of Gruenbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of ...
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Geometry and the Imagination
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David Hilbert
This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer - even after more than half a century has passed! The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, ...
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Regular Polytopes
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by
H S M Coxeter
Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.
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Crocheting Adventures with Hyperbolic Planes
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Daina Taimina
This richly illustrated book discusses non-Euclidean geometry and the hyperbolic plane in an accessible way. The author provides instructions for how to crochet models of the hyperbolic plane, pseudosphere, and catenoid/helicoids. With this knowledge, the reader has a hands-on tool for learning the properties of the hyperbolic plane and negative ...
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Euclidean and Non-Euclidean Geometry: An Analytic Approach
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by
Patrick J Ryan
This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic. The primary purpose is to acquaint the reader with the classical results of plane Euclidean and nonEuclidean geometry, congruence theorems, concurrence theorems, classification of isometries, angle addition and ...
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The Poincare Half-Plane: A Gateway to Modern
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Saul Stahl
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Janos Bolyai, Non-Euclidean Geometry, and the Nature of Space
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by
Jeremy Gray
Janos Bolyai (1802-1860) was a mathematician who changed our fundamental ideas about space. As a teenager he started to explore a set of nettlesome geometrical problems, including Euclid's parallel postulate, and in 1832 he published a 24 page paper that eventually shook the foundations of the 2000-year-old tradition of Euclidean geometry. Bolyai ...
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Thomas Reid's Inquiry: The Geometry of Visibles & the Case for Realism
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Norman Daniels
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The non-Euclidean revolution
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by
Richard J Trudeau
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 ...
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The foundations of geometry and the non-Euclidean plane
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George Edward Martin
"The Foundations of Geometry and the Non-Euclidean Plane" is a self-contained text for junior, senior, and first-year graduate courses. Historical material is interwoven with a rigorous ruler - and protractor axiomatic development of the Euclidean and hyperbolic planes. Additional topics include the classical axiomatic systems of Euclid and ...
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Topological Vector Spaces
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Helmut H Schaefer
This book is intended to be a systematic text on topological vector spaces and presupposes familiarity with the elements of general topology and linear algebra. Similarly, the elementary facts on Hilbert and Banach spaces are widely known and are not discussed in detail in this book, which is mainly addressed to those readers who have attained and ...
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Riemannian Geometry
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Peter Petersen
This book is intended for a one year course in Riemannian Geometry. It will serve as a single source, introducing students to the important techniques and theorems while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian Geometry. Instead of variational techniques, the author uses a ...
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A Hilbert space problem book
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by
Paul R. Halmos
From the Preface: 'This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks...The second part, a very short one, consists of hints...The third part, the longest, consists of solutions: proofs, answers, or ...
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Integration of One-Forms on P-Adic Analytic Spaces
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Vladimir G Berkovich
Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in the class of analytic functions. In the early 1980s, Robert Coleman discovered a way to ...
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Hyperbolic Geometry
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by
James W Anderson
The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, taking the approach that hyperbolic geometry consists of the study of those quantities invariant under the action of a natural group of ...
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Differential Geometry and Symmetric Spaces
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Sigurdur Helgason
Sigurdur Helgason's "Differential Geometry and Symmetric Spaces" was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several generations of mathematicians relied on it for its clarity and careful attention to detail. ...
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The Elements of Non-Euclidean Geometry
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by
D M Y Sommerville
Renowned for its lucid yet meticulous exposition, this text follows the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to such advanced topics as inversion and transformations. It features the relation between parataxy and parallelism, the absolute measure, the pseudosphere, and Gauss' proof of the ...
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The Nature and Power of Mathematics
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Donald M Davis
This volume explains ideas in mathematics to the non-specialist, highlighting the field's philosophical and historical interest. The main topics discussed are non-Euclidean geometry, number theory, with its application to cryptography, and fractals.
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Foundations of Hyperbolic Manifolds
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John G Ratcliffe
This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. The reader is assumed to have a basic knowledge of algebra and topology at the first year graduate level of an American university. The book is divided into three parts. The first part is concerned ...
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Non-Euclidean Geometries
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by
Andras Prekopa (Editor), Andras Prikopa (Editor), Emil Molnar (Editor)
'From nothing I have created a new different world,' wrote Janos Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical ...
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Introductory Non-Euclidean Geometry
by
Henry Parker Manning
This fine and versatile introduction to non-Euclidean geometry is appropriate for both high-school and college classes. It begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. Major topics include hyperbolic geometry, single ...
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