Taxicab Geometry: An Adventure in Non-Euclidean Geometry (Dover Books on Mathematics) - Softcover

Krause, Eugene F.

Softcover

ISBN 10: 0486252027 ISBN 13: 9780486252025

Publisher: Dover Publications, 1987

Synopsis

This entertaining, stimulating textbook offers anyone familiar with Euclidean geometry — undergraduate math students, advanced high school students, and puzzle fans of any age — an opportunity to explore taxicab geometry, a simple, non-Euclidean system that helps put Euclidean geometry in sharper perspective.
In taxicab geometry, the shortest distance between two points is not a straight line. Distance is not measured as the crow flies, but as a taxicab travels the "grid" of the city street, from block to block, vertically and horizontally, until the destination is reached. Because of this non-Euclidean method of measuring distance, some familiar geometric figures are transmitted: for example, circles become squares.
However, taxicab geometry has important practical applications. As Professor Krause points out, "While Euclidean geometry appears to be a good model of the 'natural' world, taxicab geometry is a better model of the artificial urban world that man has built."
As a result, the book is replete with practical applications of this non-Euclidean system to urban geometry and urban planning — from deciding the optimum location for a factory or a phone booth, to determining the most efficient routes for a mass transit system.
The underlying emphasis throughout this unique, challenging textbook is on how mathematicians think, and how they apply an apparently theoretical system to the solution of real-world problems.

Edition details

• Publisher: Dover Publications
• Publication date: 1987
• Language: English
• ISBN 10: 0486252027
• ISBN 13: 9780486252025
• Binding: Paperback
• Number of pages: 96