Taxicab Geometry: An Adventure in Non-Euclidean Geometry - Brossura

Krause, Eugene F.

Brossura

ISBN 10: 0486252027 ISBN 13: 9780486252025

Casa editrice: Dover Pubns, 1987

Riassunto

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.

Su questo libro

Product Description

Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Topics include applications to urban geography and planning plus comparisons to Euclidean geometry. Every principle is illustrated and clarified with numerous research problems, exercises, and graphs. Selected answers to problems.

Contenuti

1 what is taxicab geometry? 2 some applications 3 some geometric figures 4 distance from a point to a line 5 triangles 6 further applications to urban geography 7 some directions for further research appendix taxicab geometry and euclidean geometry compared selected answers index

Dettagli dell?edizione

• Editore: Dover Pubns
• Data di pubblicazione: 1987
• Lingua: Inglese
• ISBN 10: 0486252027
• ISBN 13: 9780486252025
• Rilegatura: Copertina flessibile
• Numero di pagine: 96
• Contatto del produttore: non disponibile
• Persona responsabile: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italia