Taxicab

The Last Recreations collects the final works of Martin Gardner, the renowned "Mathematical Games" columnist for Scientific American. No prior knowledge of mathematics are necessary here; all will enjoy learning about topics ranging from Bulgarian solitaire to taxicab geometry, with experienced expositor Gardner as guide. Letters and updates concerning his column are also included in this book.

Twenty years ago, while riding in the back of a New York City taxicab, syndicated columnist and business consultant David J. Pollay had an awakening-and he converted the lesson he learned that day into a life philosophy: By letting other people's “garbage”-their negativity-simply “pass by,” and not dumping garbage on others, you can become happier and more successful, both personally and professionally.

This book is intended as a first rigorous course in geometry. As the title indicates, we have adopted Birkhoff's metric approach (i.e., through use of real numbers) rather than Hilbert's synthetic approach to the subject. Throughout the text we illustrate the various axioms, definitions, and theorems with models ranging from the familiar Cartesian plane to the Poincare upper half plane, the Taxicab plane, and the Moulton plane. We hope that through an intimate acquaintance with examples (and a model is just an example), the reader will obtain a real feeling and intuition for non­ Euclidean (and in particular, hyperbolic) geometry. From a pedagogical viewpoint this approach has the advantage of reducing the reader's tendency to reason from a picture.