A
book written by
John H. Conway and
Richard K. Guy in 1996.
ISBN 0-387-97993-X. In the
preface, as should be expected, they mention
Deuteronomy and
Joshua as possible
sequels, pending the success of this book.
As a book it is fairly well-ordered, yet also sporadic.
The Pythagorean theorem is discussed, not in a chapter titled "Famous Families of Numbers," but rather in one named "Further Fruitfulness of Fractions." It seems strange to me that a
theorem so often associated with
integers is associated with
fractions.
The
basic theme of the book is numbers. Aside from the everyday "
well, duh", both number types and specific numbers are discussed, including
primes,
Lucas and Fibonacci numbers,
irrational numbers,
imaginary numbers,
transcendental numbers and
infinity. The chapter titles are:
- The Romance of Numbers
- Figures from figures: Doing Arithmetic and Algebra by Geometry
- What Comes Next?
- Famous Families of Numbers
- The Primacy of Primes
- Further Fruitfulness of Fractions
- Geometric Problems and Algebraic Numbers
- Imagining Imaginary Numbers
- Some Transcendental Numbers
- Infinite and Infinitesimal Numbers
Warning: This is not a
proof-based book. Many things are simply stated. As my
math professor put it, "This book doesn't have a very good
bibliography."