The Elements Of Non Euclidean Geometry
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The Elements Of Non Euclidean Geometry
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Author : Julian Lowell Coolidge, PhD
language : en
Publisher:
Release Date : 2020-06-04
The Elements Of Non Euclidean Geometry written by Julian Lowell Coolidge, PhD and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-04 with categories.
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.
The Elements Of Non Euclidean Geometry
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Author : D. M.Y. Sommerville
language : en
Publisher: Courier Corporation
Release Date : 2012-05-24
The Elements Of Non Euclidean Geometry written by D. M.Y. Sommerville and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.
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.
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.
The Elements Of Non Euclidean Geometry By D M Y Sommerville
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Author : Duncan M'Laren Young Sommerville
language : en
Publisher:
Release Date : 1958
The Elements Of Non Euclidean Geometry By D M Y Sommerville written by Duncan M'Laren Young Sommerville and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Geometry, Non-Euclidean categories.
The Elements Of Non Euclidean Geometry
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Author : Julian Lowell Coolidge
language : en
Publisher:
Release Date : 1927
The Elements Of Non Euclidean Geometry written by Julian Lowell Coolidge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1927 with Geometry, Non-Euclidean categories.
The Elements Of Non Euclidean Geometry
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Author : Julian Lowell Coolidge
language : en
Publisher: Forgotten Books
Release Date : 2015-06-24
The Elements Of Non Euclidean Geometry written by Julian Lowell Coolidge and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-24 with Mathematics categories.
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.
Elements Of Non Euclidean Geometry
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Author : JULIAN LOWELL. COOLIDGE
language : en
Publisher:
Release Date : 2018
Elements Of Non Euclidean Geometry written by JULIAN LOWELL. COOLIDGE and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
The Elements Of Non Euclidean Geometry Classic Reprint
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Author : Duncan M'Laren Young Sommerville
language : en
Publisher: Forgotten Books
Release Date : 2017-09-12
The Elements Of Non Euclidean Geometry Classic Reprint written by Duncan M'Laren Young Sommerville and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-12 with Mathematics categories.
Excerpt from The Elements of Non-Euclidean Geometry The present work is an extension and elaboration of a course of lectures on non-euclidean Geometry which I delivered at the Colloquium held under the auspices of the Edinburgh Mathematical Society in August, 1913. 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
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Author : Duncan M'Laren Young Sommerville
language : en
Publisher:
Release Date : 1914
The Elements Of Non Euclidean Geometry written by Duncan M'Laren Young Sommerville and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1914 with Bell's mathematical series for schools and colleges categories.
Elements Of Non Euclidean Geometry
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Author :
language : en
Publisher:
Release Date : 1919
Elements Of Non Euclidean Geometry written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1919 with categories.