Two-dimensional geometries : a problem-solving approach /

• Main Author: Clemens, C. Herbert (Charles Herbert), 1939- (συγγραφέας.)
• Format: Book
• Language: English
• Published: Providence : American Mathematical Society, 2019.
• Series: Pure and applied undergraduate texts (American Mathematical Society) 34.
• Subjects: Γεωμετρία, Περιγραφική

Table of Contents:

• 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.