Synopses & Reviews
A relaxed and informal presentation conveying the joy of mathematical discovery and insight. Frequent questions lead readers to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful ideas. The text presents eight topics that illustrate the unity of mathematical thought as well as the diversity of mathematical ideas. Drawn from both "pure" and "applied" mathematics, they include: spirals in nature and in mathematics; the modern topic of fractals and the ancient topic of Fibonacci numbers; Pascals Triangle and paper folding; modular arithmetic and the arithmetic of the infinite. The final chapter presents some ideas about how mathematics should be done, and hence, how it should be taught. Presenting many recent discoveries that lead to interesting open questions, the book can serve as the main text in courses dealing with contemporary mathematical topics or as enrichment for other courses. It can also be read with pleasure by anyone interested in the intellectually intriguing aspects of mathematics.
In a relaxed, informal style, this book conveys the joy of mathematical discovery and insight, helping readers to see mathematics as an accessible world of thought. Explores spirals, fractals, Fibonacci numbers, Pascal's Triangle and paper folding, and more.
Focusing Your Attention The purpose of this book is Cat least) twofold. First, we want to show you what mathematics is, what it is about, and how it is done-by those who do it successfully. We are, in fact, trying to give effect to what we call, in Section 9.3, our basic principle of mathematical instruction, asserting that "mathematics must be taught so that students comprehend how and why mathematics is qone by those who do it successfully./I However, our second purpose is quite as important. We want to attract you-and, through you, future readers-to mathematics. There is general agreement in the (so-called) civilized world that mathematics is important, but only a very small minority of those who make contact with mathematics in their early education would describe it as delightful. We want to correct the false impression of mathematics as a combination of skill and drudgery, and to re inforce for our readers a picture of mathematics as an exciting, stimulating and engrossing activity; as a world of accessible ideas rather than a world of incomprehensible techniques; as an area of continued interest and investigation and not a set of procedures set in stone."
Table of Contents
1. Going Down the Drain 2. A Far Nicer Arithmetic 3. Fibonacci and Lucas Numbers 4. Paper Folding and Number Theory 5. Quilts and Other Decorative Geometries 6. Pascal, Euler, Triangles, and Windmills 7. Hair and Beyond 8. An Introduction to the Mathematics of Fractal Geometry 9. Some of Our Reflections