Two-Dimensional Geometries

A Problem-Solving Approach

C. Herbert Clemens (Autor)

Buch | Hardcover

142 Seiten

2019
American Mathematical Society (Verlag)
978-1-4704-4760-1 (ISBN)

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Uses a problem-solving approach to actively engage students in the learning process. The book bridges the study of plane geometry and the study of curves and surfaces of non-constant curvature in three-dimensional Euclidean space.

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.

C. Herbert Clemens, Ohio State University, Columbus, OH.

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

Erscheinungsdatum	02.05.2019
Reihe/Serie	Pure and Applied Undergraduate Texts
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	450 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-4760-6 / 1470447606
ISBN-13	978-1-4704-4760-1 / 9781470447601
Zustand	Neuware