Download Full eBooks in PDF
Foundations Of Euclidean And Non Euclidean Geometry Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Foundations Of Euclidean And Non Euclidean Geometry book. This book definitely worth reading, it is an incredibly well-written.
Author : Ellery B. Golos
Publisher : Unknown
Page : 248 pages
File Size : 48,8 Mb
Release : 1968
Category : Geometry
ISBN : UOM:39015014352952
Author : Richard L. Faber
Publisher : CRC Press
Page : 352 pages
File Size : 44,6 Mb
Release : 1983-01-28
Category : Mathematics
ISBN : 0824717481
Author : G.E. Martin
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461257257
This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref erence if necessary.
Author : L. Redei
Publisher : Elsevier
Page : 412 pages
File Size : 41,8 Mb
Release : 2014-07-15
Category : Mathematics
ISBN : 9781483282701
Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein aims to remedy the deficiency in geometry so that the ideas of F. Klein obtain the place they merit in the literature of mathematics. This book discusses the axioms of betweenness, lattice of linear subspaces, generalization of the notion of space, and coplanar Desargues configurations. The central collineations of the plane, fundamental theorem of projective geometry, and lines perpendicular to a proper plane are also elaborated. This text likewise covers the axioms of motion, basic projective configurations, properties of triangles, and theorem of duality in projective space. Other topics include the point-coordinates in an affine space and consistency of the three geometries. This publication is beneficial to mathematicians and students learning geometry.
Author : Patrick J. Ryan
Publisher : Cambridge University Press
Page : 237 pages
File Size : 50,7 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 : Patrick J. Ryan
Publisher : Cambridge University Press
Page : 240 pages
File Size : 46,6 Mb
Release : 1986-06-27
Category : Mathematics
ISBN : 0521276357
A thorough analysis of the fundamentals of plane geometry The reader is provided with an abundance of geometrical facts such as the classical results of plane Euclidean and non-Euclidean geometry, congruence theorems, concurrence theorems, classification of isometries, angle addition, trigonometrical formulas, etc.
Author : László Rédei,Felix Klein
Publisher : Unknown
Page : 400 pages
File Size : 51,9 Mb
Release : 1968
Category : Geometry
ISBN : 1483229904
Author : H. S. M. Coxeter
Publisher : Cambridge University Press
Page : 362 pages
File Size : 55,7 Mb
Release : 1998-09-17
Category : Mathematics
ISBN : 0883855224
A reissue of Professor Coxeter's classic text on non-Euclidean geometry. It surveys real projective geometry, and elliptic geometry. After this the Euclidean and hyperbolic geometries are built up axiomatically as special cases. This is essential reading for anybody with an interest in geometry.
Author : I.M. Yaglom
Publisher : Springer
Page : 338 pages
File Size : 50,9 Mb
Release : 1979-02-28
Category : Gardening
ISBN : UOM:39015017136782
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 : Harold E. Wolfe
Publisher : Courier Corporation
Page : 272 pages
File Size : 42,5 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780486320373
College-level text for elementary courses covers the fifth postulate, hyperbolic plane geometry and trigonometry, and elliptic plane geometry and trigonometry. Appendixes offer background on Euclidean geometry. Numerous exercises. 1945 edition.
Author : Maria Helena Noronha
Publisher : Unknown
Page : 440 pages
File Size : 40,8 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 : Marvin J. Greenberg
Publisher : WH Freeman
Page : 500 pages
File Size : 54,6 Mb
Release : 2007-09-28
Category : Mathematics
ISBN : 0716799480
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 : Boris A. Rosenfeld
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 42,6 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 : Clarence Raymond Wylie
Publisher : Unknown
Page : 356 pages
File Size : 43,9 Mb
Release : 1964
Category : Geometry
ISBN : UOM:39015049076121
Author : Roberto Bonola
Publisher : Courier Corporation
Page : 452 pages
File Size : 41,9 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.