Taxicab Geometry: An Adventure in Non-Euclidean Geometry

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Overview

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.

Develops a simple non-Euclidean geometry and explores some of its practical applications through graphs, research problems, and exercises. Includes selected answers.

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Product Details

  • ISBN-13: 9780486252025
  • Publisher: Dover Publications
  • Publication date: 1/1/1987
  • Pages: 96
  • Sales rank: 474,029
  • Product dimensions: 5.45 (w) x 8.48 (h) x 0.27 (d)

Table of Contents

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
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