Taxicab Geometry: An Adventure in Non-Euclidean Geometry (Dover Books on Mathematics) by Eugene F. Krause (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐An interesting and very thought provoking introduction to one type of non-Euclidean geometry. This book is suitable for anyone who already knows the Pythagorean Theorem as it uses a variation for the basis of the calculations needed to complete the exercises in the book. It is very easy to read and understand the concepts. Some of the answers to the end of chapter questions are included. The chapters are short and the material is logically presented. Also, it is an interesting book for math lovers who would like to expand their mathematical understanding of how everyday travel works instead of using as the crow flies estimates.

⭐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.

⭐A curious and different look at graph theory based on grids. Ideas presented by the author will not be seen in the usual math texts. Writing is clear, direct, and not extensive (on purpose); as stated the author wants us to explore the concepts.Not trying the exercises will limit a clear development and progress within the topic. Good for those interested in puzzles, problem solving, or math. Not a PhD exposition, but more on the lines of Martin Gardner specific to one topic.Recommended for those that like math -thinking, and exploring; and really kind of fun once you get the graph paper out.

⭐Bought this as gift for someone else

⭐This book covers the basics of “taxicab” geometry as a simple non-euclidean geometry well, but misses entirely the actual applications in electronics, path following, etc.

⭐It’s been around for decades, but you can’t beat this little book for potential student projects. And as a Dover publication, the price is right also.

⭐A challenging mind-tweaker, so deceptively simple in concept and as commonplace in its application as traveling our city streets. When did you last delve into a non-Euclidean world with contradictory feelings of familiarity and astonishment? Me–never! Short chapters put a concept to work that you explore through exercises. Get some graph paper and discover Ideal City and its geometry of square circles and area-lines. Accessible for those of any age who have a moderate interest in things geometric.

⭐This book is one of the reasons I pursued a career in math. I’ve re-read it a few times over the last decade and even referenced it at work to educate others on ways to think outside the euclidean box.

⭐Un’introduzione elemntare alle geometrie non-euclidee, forse troppo elementare tanto non essere certi di quale dovrebbe essere il pubblico a cui si rivolge.

⭐

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