Euclidean And Non Euclidean Geometry

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Euclidean And Non Euclidean Geometry International Student Edition

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Author : Patrick J. Ryan
language : en
Publisher: Cambridge University Press
Release Date : 2009-09-04

Euclidean And Non Euclidean Geometry International Student Edition written by Patrick J. Ryan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-04 with Mathematics categories.

This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.

Euclidean And Non Euclidean Geometries

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Author : Maria Helena Noronha
language : en
Publisher:
Release Date : 2002

Euclidean And Non Euclidean Geometries written by Maria Helena Noronha and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

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.

A History Of Non Euclidean Geometry

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Author : Boris A. Rosenfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-08

A History Of Non Euclidean Geometry written by Boris A. Rosenfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-08 with Mathematics categories.

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.

A Simple Non Euclidean Geometry And Its Physical Basis

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Author : Isaak Moiseevic Jaglom
language : en
Publisher:
Release Date : 1979

A Simple Non Euclidean Geometry And Its Physical Basis written by Isaak Moiseevic Jaglom and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.

Non Euclidean Geometry Sixth Edition

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Author : H. S. M. Coxeter
language : en
Publisher: American Mathematical Soc.
Release Date : 1998-12-31

Non Euclidean Geometry Sixth Edition written by H. S. M. Coxeter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-31 with Mathematics categories.

A reissue of Professor Coxeter's classic text on non-euclidean geometry.

Euclidean And Non Euclidean Geometries

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Author : Marvin J. Greenberg
language : en
Publisher: WH Freeman
Release Date : 2007-09-28

Euclidean And Non Euclidean Geometries written by Marvin J. Greenberg and has been published by WH Freeman this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-28 with Mathematics categories.

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.

The Foundations Of Geometry And The Non Euclidean Plane

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Author : G.E. Martin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Foundations Of Geometry And The Non Euclidean Plane written by G.E. Martin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Geometry A Comprehensive Course

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Author : Dan Pedoe
language : en
Publisher: Courier Corporation
Release Date : 2013-04-02

Geometry A Comprehensive Course written by Dan Pedoe and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-02 with Mathematics categories.

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.

Geometry Euclid And Beyond

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Author : Robin Hartshorne
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Geometry Euclid And Beyond written by Robin Hartshorne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.

In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. For a one-semester course such as I teach, Chapters 1 and 2 form the core material, which takes six to eight weeks.