The Elements Of Non Euclidean Geometry

The Elements of Non Euclidean Geometry PDF
Author: D. M.Y. Sommerville
Publisher: Courier Corporation
ISBN: 0486154580
Size: 67.32 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 288
View: 2221

Get Book

The Elements Of Non Euclidean Geometry

by D. M.Y. Sommerville, The Elements Of Non Euclidean Geometry Books available in PDF, EPUB, Mobi Format. Download The Elements Of Non Euclidean Geometry book, Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.



The Elements Of Non Euclidean Geometry

The Elements of Non Euclidean Geometry PDF
Author: Julian Lowell Coolidge
Publisher:
ISBN: 9781672571258
Size: 27.89 MB
Format: PDF, ePub, Mobi
Category :
Languages : en
Pages : 250
View: 3822

Get Book

The Elements Of Non Euclidean Geometry

by Julian Lowell Coolidge, The Elements Of Non Euclidean Geometry Books available in PDF, EPUB, Mobi Format. Download The Elements Of Non Euclidean Geometry book, The heroic age of non-euclidean geometry is passed. It is long since the days when Lobatchewsky timidly referred to his system as an 'imaginary geometry', and the new subject appeared as a dangerous lapse from the orthodox doctrine of Euclid. The attempt to prove the parallel axiom by means of the other usual assumptions is now seldom undertaken, and those who do undertake it, are considered in the class with circle-squarers and searchers for perpetual motion- sad by-products of the creative activity of modern science. In this, as in all other changes, there is subject both for rejoicing and regret. It is a satisfaction to a writer on non-euclidean geometry that he may proceed at once to his subject, without feeling any need to justify himself, or, at least, any more need than any other who adds to our supply of books. On the other hand, he will miss the stimulus that comes to one who feels that he is bringing out something entirely new and strange. The subject of non-euclidean geometry is, to the mathematician, quite as well established as any other branch of mathematical science; and, in fact, it may lay claim to a decidedly more solidbasis than some branches, such as the theory of assemblages, or the analysis situs.



The Elements Of Non Euclidean Geometry Classic Reprint

The Elements of Non Euclidean Geometry  Classic Reprint  PDF
Author: Julian Lowell Coolidge
Publisher: Forgotten Books
ISBN: 9780266497806
Size: 80.40 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 318
View: 7745

Get Book

The Elements Of Non Euclidean Geometry Classic Reprint

by Julian Lowell Coolidge, The Elements Of Non Euclidean Geometry Classic Reprint Books available in PDF, EPUB, Mobi Format. Download The Elements Of Non Euclidean Geometry Classic Reprint book, Excerpt from The Elements of Non-Euclidean Geometry In this, as in all other changes, there is subject both for rejoicing and regret. It is a satisfaction to a writer on non-euclidean geometry that he may proceed at once to his subject, without feeling any need to justify himself, or, at least, any more need than any other who adds to our supply of books. On the other hand, he will miss the stimulus that comes to one who feels that he is bringing out something entirely new and strange. The subject of non-euclidean geometry is, to the mathematician, quite as well established as any other branch of mathematical science; and, in fact, it may lay claim to a decidedly more solid basis than some branches, such as the theory of assemblages, or the analysis situs. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.



The Elements Of Non Euclidean Geometry

The Elements of Non Euclidean Geometry PDF
Author: Julian Lowell Coolidge
Publisher: Forgotten Books
ISBN: 9781330306765
Size: 17.64 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 312
View: 7330

Get Book

The Elements Of Non Euclidean Geometry

by Julian Lowell Coolidge, The Elements Of Non Euclidean Geometry Books available in PDF, EPUB, Mobi Format. Download The Elements Of Non Euclidean Geometry book, Excerpt from The Elements of Non-Euclidean Geometry The heroic age of non-euclidean geometry is passed. It is long since the days when Lobachevsky timidly referred to his system as an 'imaginary geometry', and the new subject appeared as a dangerous lapse from the orthodox doctrine of Euclid. The attempt to prove the parallel axiom by means of the other usual assumptions is now seldom undertaken, and those who do undertake it, are considered in the class with circle-squarers and searchers for perpetual motion - sad by-products of the creative activity of modern science. In this, as in all other changes, there is subject both for rejoicing and regret. It is a satisfaction to a writer on non-euclidean geometry that he may proceed at once to his subject, without feeling any need to justify himself, or, at least, any more need than any other who adds to our supply of books. On the other hand, he will miss the stimulus that comes to one who feels that he is bringing out something entirely now and strange. The subject of non-euclidean geometry is, to the mathematician, quite as well established as any other branch of mathematical science; and, in fact, it may lay claim to a decidedly more solid basis than some branches, such as the theory of assemblages, or the analysis situs. Recent books dealing with non-euclidean geometry fall naturally into two classes. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.



The Elements Of Non Euclidean Geometry

The Elements of Non Euclidean Geometry PDF
Author: Julian Lowell Coolidge, PhD
Publisher:
ISBN:
Size: 56.46 MB
Format: PDF, ePub
Category :
Languages : en
Pages : 274
View: 6954

Get Book

The Elements Of Non Euclidean Geometry

by Julian Lowell Coolidge, PhD, The Elements Of Non Euclidean Geometry Books available in PDF, EPUB, Mobi Format. Download The Elements Of Non Euclidean Geometry book, In this book Dr. Coolidge explains non-Euclidean geometry which consists of two geometries based on axioms closely related to those specifying Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises when either the metric requirement is relaxed, or the parallel postulate is replaced with an alternative one. In the latter case one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras which give rise to kinematic geometries that have also been called non-Euclidean geometry. The essential difference between the metric geometries is the nature of parallel lines. Euclid's fifth postulate, the parallel postulate, is equivalent to Playfair's postulate, which states that, within a two-dimensional plane, for any given line l and a point A, which is not on l, there is exactly one line through A that does not intersect l. In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting l, while in elliptic geometry, any line through A intersects l. Another way to describe the differences between these geometries is to consider two straight lines indefinitely extended in a two-dimensional plane that are both perpendicular to a third line: In Euclidean geometry, the lines remain at a constant distance from each other (meaning that a line drawn perpendicular to one line at any point will intersect the other line and the length of the line segment joining the points of intersection remains constant) and are known as parallels. In hyperbolic geometry, they "curve away" from each other, increasing in distance as one moves further from the points of intersection with the common perpendicular; these lines are often called ultraparallels. In elliptic geometry, the lines "curve toward" each other and intersect.



A Simple Non Euclidean Geometry And Its Physical Basis

A Simple Non Euclidean Geometry and Its Physical Basis PDF
Author: I.M. Yaglom
Publisher: Springer Science & Business Media
ISBN: 146126135X
Size: 18.37 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 307
View: 1219

Get Book

A Simple Non Euclidean Geometry And Its Physical Basis

by I.M. Yaglom, A Simple Non Euclidean Geometry And Its Physical Basis Books available in PDF, EPUB, Mobi Format. Download A Simple Non Euclidean Geometry And Its Physical Basis book, 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.