Author: Duncan M'Laren Young SommervillePublisher:
ISBN:
Category : Geometry, Non-Euclidean
Languages : en
Pages : 291
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: Julian Lowell CoolidgePublisher:
ISBN:
Category : Geometry, Non-Euclidean
Languages : en
Pages : 300
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: 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.
The Elements of Non-Euclidean Geometry
Author: Julian Lowell CoolidgePublisher: Createspace Independent Publishing Platform
ISBN: 9781547058419
Category :
Languages : en
Pages : 282
Book Description
The Elements of non-Euclidean Geometry by Julian Lowell Coolidge
The Elements of Non-Euclidean Geometry
Author: Duncan M'Laren Young SommervillePublisher: Palala Press
ISBN: 9781354300060
Category :
Languages : en
Pages : 296
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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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.
The Elements of Non-Euclidean Geometry, By D.M.Y. Sommerville
Author: Duncan M'Laren Young SommervillePublisher:
ISBN:
Category : Geometry, Non-Euclidean
Languages : en
Pages : 274
Book Description
The Elements of Non-Euclidean Plane Geometry and Trigonometry
Author: Horatio Scott CarslawPublisher:
ISBN:
Category : Geometry
Languages : en
Pages : 193
Book Description
Author: