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Taxicab Geometry: An Adventure in Non-Euclidean Geometry (Dover Books on Mathematics), by Eugene F. Krause
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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.
- Sales Rank: #406479 in Books
- Published on: 1987-01-01
- Released on: 1987-01-01
- Original language: English
- Number of items: 1
- Dimensions: 8.48" h x .27" w x 5.45" l, .33 pounds
- Binding: Paperback
- 96 pages
Most helpful customer reviews
20 of 21 people found the following review helpful.
Excellent for high school teachers and students
By dfromchicago
I use the ideas in this book in my mathematics teaching in high school. Students learn to think of the world as Euclidean through most of their instruction; Taxicab Geoemetry gives teachers a very straghtforward way to introduce non-Eucliean Geometry. Admittedly, this book is not thorough, and it is very open ended (which I consider to be positive). Nevertheless, for its intended audience it is outstanding.
31 of 35 people found the following review helpful.
Excellent for what it is
By Robert Street
Before purchasing this book, realize what it is. This is a book about non-euclidean geometry. Specifically, a specialized form of non-euclidian geometry affectionately referred to as taxi-cab geometry. This is not a table top book, but is a book for mathemeticians and those interested in mathematics. Others need not apply (regardless of how interesting the topic is). This is an excellent introduction to non-euclidean geometry because it strips away common misconceptions about the nature of non-euclidean geometries. This text is excellent for grade school children and those who would like to branch into more advanced non-euclidean geometries like hyperbolic.
3 of 3 people found the following review helpful.
Fun little book!
By Mike W.
The book is only $6.00 and it describes a non-euclidean geometry - it's hard to go wrong! This is really more of a workshop book - the math that's in it is pretty darn simple, yet, it encourages a certain mathematical exploration. So, if you're getting burned out on Calculus and the other heavy stuff, pick this gem up (Did I mention it's only $6.00?) and do what the original mathematicians did: Play with math.
My only problem with the book, is that some of the chapters could use some more detail - on the other hand, it does encourage the reader to think a bit more deeply about what's being presented.
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