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Author : Patrick J. Ryan
Publisher : Cambridge University Press
Page : 237 pages
File Size : 48,8 Mb
Release : 2009-09-04
Category : Mathematics
ISBN : 9780521127073
This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.
Author : Marvin J. Greenberg
Publisher : Macmillan
Page : 669 pages
File Size : 48,5 Mb
Release : 2008-08-15
Category : Mathematics
ISBN : 9781429281331
This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert. Appropriate for liberal arts students, prospective high school teachers, math. majors, and even bright high school students. The first eight chapters are mostly accessible to any educated reader; the last two chapters and the two appendices contain more advanced material, such as the classification of motions, hyperbolic trigonometry, hyperbolic constructions, classification of Hilbert planes and an introduction to Riemannian geometry.
Author : Marvin J. Greenberg
Publisher : Macmillan
Page : 512 pages
File Size : 48,9 Mb
Release : 1993-07-15
Category : Mathematics
ISBN : 0716724464
This classic text provides overview of both classic and hyperbolic geometries, placing the work of key mathematicians/ philosophers in historical context. Coverage includes geometric transformations, models of the hyperbolic planes, and pseudospheres.
Author : Maria Helena Noronha
Publisher : Unknown
Page : 440 pages
File Size : 44,8 Mb
Release : 2002
Category : Mathematics
ISBN : UOM:39015053380005
This book develops a self-contained treatment of classical Euclidean geometry through both axiomatic and analytic methods. Concise and well organized, it prompts readers to prove a theorem yet provides them with a framework for doing so. Chapter topics cover neutral geometry, Euclidean plane geometry, geometric transformations, Euclidean 3-space, Euclidean n-space; perimeter, area and volume; spherical geometry; hyperbolic geometry; models for plane geometries; and the hyperbolic metric.
Author : Henry Parker Manning
Publisher : Courier Corporation
Page : 110 pages
File Size : 41,7 Mb
Release : 2005-02-18
Category : Mathematics
ISBN : 9780486442624
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 elliptic geometry, and analytic non-Euclidean geometry. 1901 edition.
Author : Marvin J. Greenberg
Publisher : Unknown
Page : 674 pages
File Size : 54,6 Mb
Release : 2020-10-22
Category : Mathematics
ISBN : 4871870030
Captain Ahab has an obsessive search for the Great White Whale who had bitten off his leg at the knee.
Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 225 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209294
The geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.
Author : Boris A. Rosenfeld
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 52,9 Mb
Release : 2012-09-08
Category : Mathematics
ISBN : 9781441986801
The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.
Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 44,7 Mb
Release : 2005-08-09
Category : Mathematics
ISBN : 9780387255309
This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises
Author : Michael McDaniel
Publisher : Universal-Publishers
Page : 150 pages
File Size : 49,9 Mb
Release : 2015-02-05
Category : Geometrical constructions
ISBN : 9781627340281
"'Geometry by construction' challenges its readers to participate in the creation of mathematics. The questions span the spectrum from easy to newly published research and so are appropriate for a variety of students and teachers. From differentiation in a high school course through college classes and into summer research, any interested geometer will find compelling material"--Back cover.
Author : Dan Pedoe
Publisher : Courier Corporation
Page : 466 pages
File Size : 55,9 Mb
Release : 2013-04-02
Category : Mathematics
ISBN : 9780486131733
Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.
Author : I.M. Yaglom
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461261353
There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflec tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. The principal reason for the interest in hyperbolic geometry is the important fact of "non-uniqueness" of geometry; of the existence of many geometric systems.
Author : Roberto Bonola
Publisher : Courier Corporation
Page : 452 pages
File Size : 50,7 Mb
Release : 2012-08-15
Category : Mathematics
ISBN : 9780486155036
Examines various attempts to prove Euclid's parallel postulate — by the Greeks, Arabs, and Renaissance mathematicians. It considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, others. Includes 181 diagrams.
Author : András Prékopa,Emil Molnár
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 54,7 Mb
Release : 2006-06-03
Category : Mathematics
ISBN : 9780387295558
"From nothing I have created a new different world," wrote János 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 theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.
Author : EISENREICH
Publisher : Elsevier
Page : 274 pages
File Size : 48,8 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483295312
An Introduction to Non-Euclidean Geometry covers some introductory topics related to non-Euclidian geometry, including hyperbolic and elliptic geometries. This book is organized into three parts encompassing eight chapters. The first part provides mathematical proofs of Euclid’s fifth postulate concerning the extent of a straight line and the theory of parallels. The second part describes some problems in hyperbolic geometry, such as cases of parallels with and without a common perpendicular. This part also deals with horocycles and triangle relations. The third part examines single and double elliptic geometries. This book will be of great value to mathematics, liberal arts, and philosophy major students.