Mathematical Reflections: In a Room with Many Mirrors

✍ Scribed by Peter Hilton, Derek Holton, Jean Pedersen (auth.)

• Publisher: Springer-Verlag New York
• Year: 1997
• Tongue: English
• Leaves: 366
• Series: Undergraduate Texts in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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

Front Matter....Pages i-xvi
Going Down the Drain....Pages 1-24
A Far Nicer Arithmetic....Pages 25-60
Fibonacci and Lucas Numbers....Pages 61-86
Paper-Folding and Number Theory....Pages 87-142
Quilts and Other Real-World Decorative Geometry....Pages 143-184
Pascal, Euler,Triangles,Windmills,.......Pages 185-248
Hair and Beyond....Pages 249-276
An Introduction to the Mathematics of Fractal Geometry....Pages 277-322
Some of Our Own Reflections....Pages 323-338
Back Matter....Pages 339-352

✦ Subjects

Mathematics, general