# Biscuits of Number Theory

Share this page *Edited by *
*Arthur T. Benjamin; Ezra Brown*

MAA Press: An Imprint of the American Mathematical Society

In Biscuits of Number Theory, the
editors have chosen articles that are exceptionally well-written and
that can be appreciated by anyone who has taken (or is taking) a first
course in number theory. This book could be used as a textbook
supplement for a number theory course, especially one that requires
students to write papers or do outside reading.

The editors
give examples of some of the possibilities. The collection is divided
into seven chapters: Arithmetic; Primes; Irrationality and Continued
Fractions; Sums of Squares and Polygonal Numbers; Fibonacci Numbers;
Number-Theoretic Functions; and Elliptic Curves, Cubes and Fermat's
Last Theorem. As with any anthology, you don't have to read the
Biscuits in order. Dip into them anywhere: pick something from the
table of contents that strikes your fancy, and have at it. If the end
of an article leaves you wondering what happens next, then by all
means dive in and do some research. You just might discover something
new!

#### Reviews & Endorsements

A collection of accessible and even profound essays on number theory gleaned from a wide variety of writers and journals--everyone from Euler to Quine, plus many recent popular expositions. An invigorating and generally undemanding excursion into surprise. A first rate book.

-- Bob Lockhart, London Math Society Newsletter

The authors represented include some of the best expositors of elementary number theory: Peter Borwein, Stan Wagon, Carl Pomerance, Ivan Niven, Edward Berger, Ross Honsberger, and Martin Gardent, just to name a few. … it's good when a book has some content above the level of the typical reader, because this will intrigue some readers sufficiently that they'll feel the need to learn the required material. The challenge is to have the right amount, and my feeling is that this book has a good balance of material.

-- Jeffrey Shallit, Sigact News

# Table of Contents

## Biscuits of Number Theory

- Cover Cover11
- Copyright ii3
- Title iii4
- Contents vii8
- Introduction x11
- Part I: Arithmetic 114
- Part II: Primes 5972
- Part III: Irrationality and Continued Fractions 105118
- 14. Irrationality of the Square Root of Two—A Geometric Proof 107120
- 15. Math Bite: Irrationality of Equation 109122
- 16. A Simple Proof that π is Irrational 111124
- 17. π, e and Other Irrational Numbers 113126
- 18. A Short Proof of the Simple Continued Fraction of e 115128
- 19. Diophantine Olympics and World Champions: Polynomials and Primes Down Under 121134
- 20. An Elementary Proof of the Wallis Product Formula for Pi 129142
- 21. The Orchard Problem 133146

- Part IV: Sums of Squares and Polygonal Numbers 141154
- Part V: Fibonacci Numbers 155168
- Part VI: Number-Theoretic Functions 195208
- 30. Great Moments of the Riemann zeta Function 199212
- 31. The Collatz Chameleon 217230
- 32. Bijecting Euler's Partition Recurrence 223236
- 33. Discovery of a Most Extraordinary Law of the Numbers Concerning the Sum of Their Divisors 225238
- 34. The Factorial Function and Generalizations 233246
- 35. An Elementary Proof of the Quadratic Reciprocity Law 251264

- Part VII: Elliptic Curves, Cubes and Fermat's Last Theorem 255268
- Back cover Back Cover1331