Author: Julian Lowell CoolidgePublisher:
ISBN:
Category : Geometry, Non-Euclidean
Languages : en
Pages : 300
Book Description
The Elements of Non-Euclidean Geometry
Author: Julian Lowell CoolidgePublisher:
ISBN:
Category : Geometry, Non-Euclidean
Languages : en
Pages : 300
Book Description
The Elements of Non-Euclidean Geometry
Author: Duncan M'Laren Young SommervillePublisher:
ISBN:
Category : Geometry, Non-Euclidean
Languages : en
Pages : 291
Book Description
The Elements of Non-euclidean Geometry
Author: D. M. Y. SommervillePublisher:
ISBN:
Category :
Languages : en
Pages : 274
Book Description
Elements of Non-Euclidean Geometry
Author: The Elements of Non-Euclidean Geometry
Author: Julian Lowell CoolidgePublisher:
ISBN:
Category : Geometry, Non-Euclidean
Languages : en
Pages : 291
Book Description
ELEMENTS OF NON-EUCLIDEAN GEOMETRY
Author: JULIAN LOWELL. COOLIDGEPublisher:
ISBN: 9781033719237
Category :
Languages : en
Pages : 0
Book Description
The Elements of Non-Euclidean Geometry
Author: Julian Lowell Coolidge, PhDPublisher:
ISBN:
Category :
Languages : en
Pages : 274
Book Description
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
Author: I.M. YaglomPublisher: Springer Science & Business Media
ISBN: 146126135X
Category : Mathematics
Languages : en
Pages : 326
Book Description
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.
Introduction to Non-Euclidean Geometry
Author: Harold E. WolfePublisher: Courier Corporation
ISBN: 0486320375
Category : Mathematics
Languages : en
Pages : 272
Book Description
College-level text for elementary courses covers the fifth postulate, hyperbolic plane geometry and trigonometry, and elliptic plane geometry and trigonometry. Appendixes offer background on Euclidean geometry. Numerous exercises. 1945 edition.
The Elements of Non-Euclidean Plane Geometry and Trigonometry
Author: Horatio Scott CarslawPublisher: Legare Street Press
ISBN: 9781016470438
Category :
Languages : en
Pages : 0
Book Description
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.