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.
Reihe
Sprache
Verlagsort
Zielgruppe
Maße
Höhe: 254 mm
Breite: 178 mm
Gewicht
ISBN-13
978-1-4704-4760-1 (9781470447601)
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Schweitzer Klassifikation
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