Two-dimensional Geometries: A Problem-solving Approach (Pure and Applied Undergraduate Texts) - Hardcover

C. Herbert Clemens

Hardcover

ISBN 10: 1470447606 ISBN 13: 9781470447601

Publisher: American Mathematical Society, 2019

Synopsis

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. One useful feature is that the book can be adapted to suit different audiences. The first half of the text covers plane geometry without and with Euclid's Fifth Postulate, followed by a brief synthetic treatment of spherical geometry through the excess angle formula. This part only requires a background in high school geometry and basic trigonometry and is suitable for a quarter course for future high school geometry teachers. A brief foray into the second half could complete a semester course. The second half of the text gives a uniform treatment of all the complete, simply connected, two-dimensional geometries of constant curvature, one geometry for each real number (its curvature), including their groups of isometries, geodesics, measures of lengths and areas, as well as formulas for areas of regions bounded by polygons in terms of the curvature of the geometry and the sum of the interior angles of the polygon. A basic knowledge of real linear algebra and calculus of several (real) variables is useful background for this portion of the text.

About this title

About the Author

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

Edition details

• Publisher: American Mathematical Society
• Publication date: 2019
• Language: English
• ISBN 10: 1470447606
• ISBN 13: 9781470447601
• Binding: Hardcover
• Number of pages: 142