Mathematical Reflections

1. Front Matter

   Pages i-xvi

   PDF

2. Going Down the Drain

   • Peter Hilton, Derek Holton, Jean Pedersen

   Pages 1-24

3. A Far Nicer Arithmetic

   • Peter Hilton, Derek Holton, Jean Pedersen

   Pages 25-60

4. Fibonacci and Lucas Numbers

   • Peter Hilton, Derek Holton, Jean Pedersen

   Pages 61-86

5. Paper-Folding and Number Theory

   • Peter Hilton, Derek Holton, Jean Pedersen

   Pages 87-142

6. Quilts and Other Real-World Decorative Geometry

   • Peter Hilton, Derek Holton, Jean Pedersen

   Pages 143-184

7. Pascal, Euler,Triangles,Windmills,...

   • Peter Hilton, Derek Holton, Jean Pedersen

   Pages 185-248

8. Hair and Beyond

   • Peter Hilton, Derek Holton, Jean Pedersen

   Pages 249-276

9. An Introduction to the Mathematics of Fractal Geometry

   • Peter Hilton, Derek Holton, Jean Pedersen

   Pages 277-322

10. Some of Our Own Reflections

    • Peter Hilton, Derek Holton, Jean Pedersen

    Pages 323-338

11. Back Matter

    Pages 339-352

    PDF

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.

• Algebra
• Arithmetic
• Finite
• geometry
• mathematics
• theorem

• Mathematical Sciences Department, SUNY at Binghamton, Binghamton, USA

  Peter Hilton

• Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand

  Derek Holton

• Department of Mathematics, Santa Clara University, Santa Clara, USA

  Jean Pedersen

Policies and ethics