Taxicab Geometry: An Adventure in Non-Euclidean Geometry

Rating:
Summary: Excellent for what it is
Review: 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.

Rating:
Summary: Excellent for what it is
Review: 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.

Rating:
Summary: This is a book for a math student only.
Review: I thought that this book would be about geometry of exotic (but real) places in outer space (such as a black hole, for example). Instead, it turned out to be a lethally boring book, full of math problems, that was LESS interesting than my geometry book in high school!

Rating:
Summary: Excellent for high school teachers and students
Review: 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.

Rating:
Summary: A simple, real-world example of non-Euclidean geometry
Review: Some years ago, I was employed by a company that built mapping software. One of the projects I worked on was the design of features that allowed for the computation of the shortest path from one position to another following only roads. This form of travel is similar to the taxicab geometry in that movement is restricted to lines. The only difference is that roads can be placed at any location or angle whereas the lines in taxicab geometry are equidistant and perpendicular. Think of it as the geometry of graph paper. As I constructed the program, I was struck by how so much of classical Euclidean geometry does not apply. Yet, the geometry is generally easier to understand because it is almost always how we move from place to place.
The phrase non-Euclidean geometry generally conjures up thoughts of curved space and Riemannian geometry. However, in this delightfully simple book, a natural non-Euclidean geometry is developed in great detail. Very little mathematics is needed to understand the geometry, if you can mark and understand the points on a grid of graph paper, nearly all of the topics will make sense. A large number of problems are included at the end of each chapter and solutions to many appear in an appendix.
The problems cover topics such as finding the point(s) of minimum distance between two or more points and what the taxicab analogues of circles and ellipses are. Determining the point of minimum distance between three or more points is a hard problem in standard geometry, but fairly simple in the taxicab geometry.
Geometry is the godfather of abstract mathematics, being first used to codify the parceling of land and the construction of cities. In this book, you will learn how to minimize functions based on the restrictions of traveling through cities, a task with many applications in the world.

Rating:
Summary: Disappointing
Review: Very simplistic treatment, with some results left for the reader to work through exercises. The chapters are almost non-existent, with all the book being mainly exercises.

Rating:
Summary: Disappointing
Review: Very simplistic treatment, with some results left for the reader to work through exercises. The chapters are almost non-existent, with all the book being mainly exercises.