Bibliography of Non-Euclidean Geometry

Cover of: Bibliography of Non-Euclidean Geometry | Duncan Y. Sommerville

Published by Chelsea Pub Co .

Written in English

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  • Science/Mathematics

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The Physical Object
FormatHardcover
Number of Pages410
ID Numbers
Open LibraryOL8171743M
ISBN 100828401756
ISBN 109780828401753

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Bibliography of Non-Euclidean Geometry Paperback – Octo by Duncan M'Laren Young Sommerville (Author) › Visit Amazon's Duncan M'Laren Young Sommerville Page. Find all the books, read about the author, and more. See search Author: Duncan M'Laren Young Sommerville.

Bibliography of non-Euclidean geometry, including the theory of parallels, the foundations of geometry, and space of n dimensions [Hardcover] Hardcover – January 1, by : Scot. University Sommerville, Duncan M'Laren Young,St. Andrews. BIBLIOGRAPHY OF NON EUCLIDEAN GEOMETRY 2nd edit [D M Y SOMMERVILLE] on *FREE* shipping on qualifying : D M Y SOMMERVILLE.

Bibliography: Additional Physical Format: Online version: Sommerville, Duncan M'Laren Young, Bibliography of non-Euclidean geometry. New York, Chelsea Pub.

[] (OCoLC) Document Type: Book: All Authors / Contributors: Duncan. Bibliography of non-Euclidean geometry, including the theory of parallels, the foundations of geometry, and space of n dimensions by Sommerville, Duncan M'Laren Young, ; St.

Andrews, sityPages: Cite this article. M., G. Bibliography of Non-Euclidean Geometry, including the Theory of Parallels, the Foundations of Geometry, and Space of N 89, (). Author: G. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.

Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the by: Throughout most of this book, non-Euclidean geometries in spaces of two or three dimensions are treated as specializations of real projective geometry in terms of a simple set of axioms concerning points, lines, planes, incidence, order and continuity, with no.

Throughout most of this book, non-Euclidean geometries in spaces of two or three dimensions are treated as specializations of real projective geometry in terms of a simple set of axioms concerning points, lines, planes, incidence, order and continuity, with no Cited by: 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 trigonometrical formulae.5/5(1).

Spherical Geometry (Non-Euclidean Geometry) - Math bibliographies - in Harvard style. (Non-Euclidean Geometry).

This bibliography was generated on Cite This For Me on Friday, May 6, Website. Euclid's Elements, Book I, Postulate 5 "Bibliography of Hyper-Space and Non-Euclidean Geometry" is an article from American Journal of Mathematics, Volume 1. View more articles from American Journal of Mathematics.

View this article on JSTOR. View this article's JSTOR metadata. Non-Euclidean Geometry Book Description: This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.

Playfair, J., Elements of Geometry; containing the first six books of Euclid, with two books on the geometry of solids. To which are added, elements of plane and spherical trigonometry, Bell and Bradfute, and G. and J. Robinson, London, (c,r).Cited by: euclidean and non euclidean geometry Download euclidean and non euclidean geometry or read online books in PDF, EPUB, Tuebl, and Mobi Format.

Click Download or Read Online button to get euclidean and non euclidean geometry book now. This site is like a library, Use search box in the widget to get ebook that you want.

Non-Euclidean Geometry (Dover Books on Mathematics) This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geo. Book Description: No living geometer writes more clearly and beautifully about difficult topics than world famous professor H.

Coxeter. When non-Euclidean geometry was first developed, it seemed little more than a curiosity with no relevance to the real world.

Bibliography of non-Euclidean geometry, including the theory of parallels, the foundation of geometry, and space of n dimensions. Author: Duncan M'Laren Young Sommerville ; University of St. Andrews. $\begingroup$ If you want to dig up the actual original writings, you can find quite a bit cited in Sommerville's book Bibliography of Non-Euclidean Geometry, and I suspect that most of the items in this bibliography (because of their publication age) are freely available on the internet.

$\endgroup$ – Dave L Renfro Oct 26 '15 at Non-Euclidean Geometry (Dover Books on Mathematics) Stefan Kulczycki. out of 5 stars 2. Paperback.

Geometry by Construction: Object Creation and Problem-solving in Euclidean and Non-Euclidean Geometries Michael McDaniel. out of 5 stars 8. Paperback. $ # The meaning of “elliptic” and “hyperbolic.” In ordinary Euclidean geometry, a central conic may be either an ellipse or a hyperbola.

For any central conic, the pairs of conjugate diameters belong to an involution (of lines through the centre); but it is only the hyperbola that has self-conjugate diameters (viz.

its two asymptotes).Accordingly, any involution (and so, conveniently, any. The Thirteen Books of Euclid’s Elements The Fourth Dimension and Non-Euclidean Geometry in Modern Art T L Heath Non-Euclidean Geometry: or, Three Moons in.

The non-Euclidean geometries developed along two different historical threads. The first thread started with the search to understand the movement of stars and planets in the apparently hemispherical sky. For example, Euclid (flourished c. bc) wrote about spherical geometry in his astronomical work Phaenomena.

In addition to looking to the. The simplest of these is called elliptic geometry and it is considered to be a non-Euclidean geometry due to its lack of parallel lines. By formulating the geometry in terms of a curvature tensor, Riemann allowed non-Euclidean geometry to be applied to higher dimensions.

Beltrami () was the first to apply Riemann's geometry to spaces of negative curvature. Bibliography. Page Select Answers to Selected Exercises. 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.

An Introduction to Non-Euclidean Geometry covers some. 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.1/5(1).

What gives non-Euclidean geometry its close resemblance to Euclidean geometry, and explains its name, can best be understood by looking briefly at Euclid's Elements. This book, which underlay most geometrical teaching in the West for over years, gave definitions of the basic terms in the subject and rules (called postulates) for their use.

This is an awkward position for traditional geometry to be in, and it may have opened people’s minds to the possibilities of alternatives. Certainly, two were to be produced. One, projective geometry, amplified and improved the synthetic side of geometry. The other, non-Euclidean geometry, was a new and challenging metrical geometry.

Elementary Geometry From An Advanced Viewpoint, 2nd edition, by Edwin Moise. Euclidean And Non-Euclidean Geometries, 3rd or 4th edition (either will do nicely) by Marvin Greenberg.

A Survey of Geometry by Howard Eves, 2nd edition(2 volumes) Moise is the classic text that develops Euclidean geometry using the metric postulates of G.D.

Birkoff. Basically a non-Euclidean geometry book, it provides a brief, but solid, introduction to modern geometry using analytic methods. It relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane and building on skills already known and extensively practiced : Prentice Hall, Inc.

The negatively curved non-Euclidean geometry is called hyperbolic geometry. Euclidean geometry in this classification is parabolic geometry, though the name is less-often used. Spherical geometry is called elliptic geometry, but the space of elliptic geometry is really has points = antipodal pairs on the sphere.

With this idea, two lines reallyFile Size: KB. Page 8 - If two triangles have two sides of the one equal respectively to two sides of the other, but the third side of the first greater than the third side of the second, then the included angle of the first is greater than the included angle of the second.

[Converse of Prop. XXXI.] B' b' Given A ABC and A'B'C', with b = b'; c = c'; a > a. To prove Z A> Z A'. Purchase Introduction to Non-Euclidean Geometry - 1st Edition. Print Book & E-Book. ISBNBook Edition: 1. Chicago undergraduate mathematics bibliography.

inspired by the long debate over Euclid's parallel postulate and the discovery in the late 19th century of consistent non-Euclidean geometries.

(The Gödel incompleteness theorems solved negatively one of Hilbert's famous problems.) Let me also recommend Stillwell's book Geometry of. Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the 's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from gh many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show.

70, () - Taxicab Geometry Eugene F. Krause Geometry on a grid, comparison to Euclidean geometry. 66, () - Taxicab Geometry - A Non-Euclidean Geometry Of Lattice Points Donald R.

Byrkit An axiomatic presentation of a geometry of lattice points. 64, () - János Bolyai, (born DecemKolozsvár, Hungary [now Cluj, Romania]—died JanuMarosvásárhely, Hungary [now Târgu Mureş, Romania]), Hungarian mathematician and one of the founders of non-Euclidean geometry— a geometry that differs from Euclidean geometry in its definition of parallel lines.

The discovery of a consistent alternative geometry that might correspond. Non-Euclidean Geometry first examines the various attempts to prove Euclid's parallel postulate-by the Greeks, Arabs, and mathematicians of the Renaissance.

Then, ranging through the 17th, 18th and 19th centuries, it considers the forerunners and founders of non-Euclidean geometry, such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss. In Sommerville published his compiled bibliography of works on non-euclidean geometry, and it received favorable reviews.

[8] [9] In Chelsea Publishing issued a second edition which referred to collected works then available of some of the cited mater: St Andrews University. Syntax; Advanced Search; New. All new items; Books; Journal articles; Manuscripts; Topics. All Categories; Metaphysics and Epistemology.

Nikolai Ivanovich Lobachevsky (Russian: Никола́й Ива́нович Лобаче́вский, IPA: [nʲikɐˈlaj ɪˈvanəvʲɪtɕ ləbɐˈtɕɛfskʲɪj] (); 1 December [O.S. 20 November] – 24 February [O.S. 12 February] ) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry and also his Alma mater: Kazan University.introduction to non euclidean geometry Download introduction to non euclidean geometry or read online books in PDF, EPUB, Tuebl, and Mobi Format.

Click Download or Read Online button to get introduction to non euclidean geometry book now. This site is like a library, Use search box in the widget to get ebook that you want.This textbook demonstrates the excitement and beauty of geometry.

The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of that space. The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case the key results are explained carefully, and the relationships between the /5(3).

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