Two-Dimensional Geometries: A Problem-Solving Approach

ISBN-13: 9781470447601 / Angielski

C. Herbert Clemens

Opis

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.

Spis treści

• 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