You are here

The (Fabulous) Fibonacci Numbers

Alfred S. Posamentier and Ingmar Lehmann
Prometheus Books
Publication Date: 
Number of Pages: 
[Reviewed by
Underwood Dudley
, on

The authors present many properties of Fibonacci numbers and the golden ratio in this book, intended for a general audience. None of the material is new, and its purpose is “to evoke the power and beauty of mathematics for all readers” (p. 15). The list of topics is clear from the table of contents . The authors write with enthusiasm and there are many illustrations.

Unfortunately, the book has defects. The authors repeat the stories of how the golden ratio was built into the Parthenon and Egyptian great pyramid, and that the “most pleasing rectangle” involves the golden ratio, as does the placement of peoples’ navels. George Markovsky debunked these notions in “Misconceptions about the golden ratio” (College Math. J. 23 (1992), 2-10). I would say that he had done it once and for all, but the truth is sometimes slow to catch up with gee-whiz stories.

The authors allege that Mozart had the golden ratio in mind when he was composing his piano sonatas. In “The golden section and the piano sonatas of Mozart” (Math. Mag. 68 (1993), 275-282) John F. Putz demonstrated to my satisfaction that the structure that the authors find in them was “determined, not by thoughtful design, but by uninspired randomness.”

They also repeat the numerology of the Elliott wave theory, that the stock market comports itself in accordance with Fibonacci numbers. They say (p. 182), “Before you scoff at the importance of Fibonacci numbers in the stock market, consider that Elliott, at the age of sixty-seven and without the aid of any computers, forecast the end of a bear market decline from 1933-1935 to the exact day.”

Prometheus Books publish very few mathematics books, and it shows. Type sizes in figures vary widely (p. 98) and, strangely, in displayed equations as well (p. 122). Points are referred to sometimes in Roman, sometimes in italic (p. 151) and the quality of the illustrations is variable, down to the almost illegible (p. 132). There is an unusual double ellipsis on page 164.

Indicative of the care that has gone into the book is the reference on the title page to a contributor, Herbert Hauptman, a winner of the Nobel prize in chemistry, as a “Lobel Laureate.”

There is no need for members of the MAA to read this book. Though high-school and college students and members of the general public could find some of its contents interesting, I would not recommend its purchase.

Woody Dudley taught for many years in Indiana. He now lives in Florida and does not teach any more.

A history and introduction to the Fibonacci numbers

The Fibonacci numbers and the Pascal triangle

The Fibonacci numbers and the golden ratio

The Fibonacci numbers and continued fractions

A potpourri of Fibonacci numbers applications

The Fibonacci numbers found in art and architecture

The Fibonacci numbers and musical form

The famous Binet formula for finding a particular Fibonacci number

The Fibonacci numbers and fractals.