Two-Dimensional Geometries
A Problem-Solving Approach
Published on 30. March 2019
Book
Hardback
142 pages
978-1-4704-4760-1 (ISBN)
Description
This book on two-dimensional geometry uses a problem-solving approach to actively engage students in the learning process. The aim is to guide readers through the story of the subject, while giving them room to discover and partially construct the story themselves. The book bridges the study of plane geometry and the study of curves and surfaces of non-constant curvature in three-dimensional Euclidean space.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
450 gr
ISBN-13
978-1-4704-4760-1 (9781470447601)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
C. Herbert Clemens, Ohio State University, Columbus, OH.
Content
Introduction
Neutral geometry: Euclid's postulates for plane geometry
Euclidean (plane) geometry: Rectangles and cartesian coordinates
Concurrence and circles in Euclidean geometry
Spherical geometry: Surface area and volume of the $R$-sphere in Euclidean 3-space
Usual dot-product for three-dimensional Euclidean space: Euclidean three-space as a metric space
Transformations
$K$-geometry: Changing coordinates
Uniform coordinates for the two-dimensional geometries
Return to spherical geometry: Spherical geometry from an advanced viewpoint
Hyperbolic geometry: The curvature $K$ becomes negative
Definitions
Bibliography
Index
Neutral geometry: Euclid's postulates for plane geometry
Euclidean (plane) geometry: Rectangles and cartesian coordinates
Concurrence and circles in Euclidean geometry
Spherical geometry: Surface area and volume of the $R$-sphere in Euclidean 3-space
Usual dot-product for three-dimensional Euclidean space: Euclidean three-space as a metric space
Transformations
$K$-geometry: Changing coordinates
Uniform coordinates for the two-dimensional geometries
Return to spherical geometry: Spherical geometry from an advanced viewpoint
Hyperbolic geometry: The curvature $K$ becomes negative
Definitions
Bibliography
Index