Elements Of Non Euclidean Geometry
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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
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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 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 : D. M. Y. Sommerville
language : en
Publisher: Forgotten Books
Release Date : 2015-06-02
The Elements Of Non Euclidean Geometry written by D. M. Y. 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 2015-06-02 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. Non-euclidean geometry is now a well-recognised branch of mathematics. It is the general type of geometry of homogeneous and continuous space, of which euclidean geometry is a special form. The creation or discovery of such types has destroyed the unique character of euclidean geometry and given it a setting amongst geometrical systems. There has arisen, so to speak, a science of Comparative Geometry. Special care has, therefore, been taken throughout this book to show the bearing of non-euclidean upon euclidean geometry; and by exhibiting euclidean geometry as a really degenerate form - in the sense in which a pair of straight lines is a degenerate conic - to explain the apparent want of symmetry and the occasional failure of the principle of duality, which only a study of non-euclidean geometry can fully elucidate. 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.
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.
The Elements Of Non Euclidean Geometry
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Author : Julian Lowell Coolidge
language : en
Publisher:
Release Date : 1909
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 1909 with Geometry, Non-Euclidean 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.