Dr. Fred Bortzbooks

Review of Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math

by Alex Bellos

(Free Press, 336 pages, $25.00, June 2010)

Reviewed by Dr. Fred Bortz

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A pair of F6s to start.
Then F5, F5 makes it smart.
To close out this list,
F6 plus a twist.
Math'matic limerical art!

No one loves a limerick more than scientists and mathematicians, and retired London dentist Eddy Levin thinks he knows why. The number of syllables in each line, either eight or five, are seventh and sixth in the famous Fibonacci series. (The series begins with F0=0 and F1=1, with subsequent numbers equal the sum of the preceding pair.)

Levin is one of many fascinating characters that English journalist Alex Bellos met while writing Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math.

Levin is fanatic about phi, the "golden mean" or "golden ratio," a number that has fascinated mathematicians at least as far back as the ancient Greeks. His obsession has led him to create a three-pronged device to detect instances of that ratio, which he uses "with the concentration of a rabbi preparing a circumcision."

In more than three decades of making dentures, Levin discovered that his patients' smiles looked most pleasing and natural when the ratios of the width of successive upper teeth from central incisors to first premolars was "golden."

He made that discovery after becoming aware of a famous 1509 book called The Divine Proportion by Italian mathematician Luca Pacioli, writes Bellos. "Pacioli concluded that the number was a message from God, a source of secret knowledge about the inner beauty of things."

Phi has a natural connection to Fibonacci numbers. The quotient of one Fibonacci number divided by its precursor in the series becomes closer and closer to phi, matching to three decimal places (1.618) by the time it reaches F9/F8.

Readers meet Levin in chapter 8, the ninth of twelve loosely connected chapters that roughly follow the development of more and more sophisticated mathematical ideas through history. Each chapter follows a similar pattern in which Bellos serves as an engaging tour guide who delights in sharing his adventures in mathematics, always illuminated by human stories.

Here's Looking at Euclid is full of surprises and insights from beginning to end. Beginning with chapter 0, about a French Professor who studies an Amazonian tribe with a language that has no words for numbers beyond five, it proceeds through chapters about counting, the Pythagorean theorem (including the numerological inclinations of its creator), zero, pi, algebra, mathematical games, number series, probability, and statistics.

It culminates with a chapter about non-Euclidean geometry and infinities--plural.

Even readers who know the math well enough to recognize where Bellos had to glide past some nuances will love this book for the stories. After all, it never hurts to know that "during medieval times, a pimp plus a dik got you a bumfit." But as Bellos adds in a line reminiscent of Seinfeld, "There was nothing dishonorable about this."

Physicist Fred Bortz is the author of nearly F8 books for young readers.