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The Divine Proportion

H. E. Huntley
Dover Publications
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Underwood Dudley
, on

Dover Publications mostly publishes reprints, but this book is an original, first published in 1970 and still going more or less strong. I wasn’t able to find out much about the author, who is not to be confused with the American comic book author and illustrator Ernie Hart (1910–1985) who used “H. E. Huntley” as a pseudonym. He was a teacher of physics at the University College of the Gold Coast (now the University of Ghana) who retired to his native England where, such was his devotion to teaching, he took a position at the local high school. He also played golf, badly. He was known as “Ted” so his middle name was probably Edward, but I don’t what the “H.” stands for or what the dates of his birth and death are. Perhaps someone more knowledgeable than I can add a comment to this review. Not even Wikipedia has anything to say. Why he sent his book to Dover is also a mystery.

Huntley was also the author of Dimensional Analysis (1951, reprinted by Dover, 1975) and The Faith of a Physicist (1960). He was evidently a thoroughly nice person, something that is reflected in his book. The book’s subtitle is “A Study in Mathematical Beauty”. Its purpose is to instill “the best and perhaps the only enduring reason for reading mathematics, which, in my view, is the aesthetic motive.”

The mathematical demands on readers are small. Though a derivative appears once and a geometric series is summed once, otherwise a little algebra is enough. Knowing what “e”, “log”, and “cot” stand for and what a binomial coefficient is doesn’t hurt.

His topics are, he says, simple and are more or less connected to the ratio \((1+\sqrt5)/2 \colon 1\) of the title. The Fibonacci numbers are here, along with the chambered nautilus, the parabola (beautiful, is it not?), Euler’s polyhedron formula, magic squares, Pascal’s triangle, sunflower seeds, and so on.

He rambles here and there, including now and then prose about beauty, philosophy, and Carl Jung, of whom he was a fan. In another review, Jacob Bronowski (1908–1974) said it as well as I can: “This is a browser’s book — a happy, untidy traveling or bedside book for those who know how to enjoy the charm of numbers and shapes.”

It’s unusual for a typographical error to endure for forty-five years, but the last equation on page 99 is wrong.

Huntley finishes with a rhetorical flourish, comparing mathematical beauty to beauty in the physical world:

Nature’s beauty dies. The day dawns when the nautilus is no more. The rainbow passes, the flower fades, the mountain crumbles, the star goes cold. But beauty in mathematics — the divine proportion, the golden rectangle, spira mirabilis — endures for evermore.

I can go along with that. If you can too, you may enjoy this book.

Woody Dudley retired from teaching in 2004 but did not take up golf. While on the job he made only minimal efforts to convince students that mathematics is beautiful, knowing that they would succeed with only a few and for the many would more likely convince them that teachers of mathematics are weird.

The table of contents is not available.

Comments's picture

Here's a lovely quote from this book:

The enjoyment of beauty in mathematics is for the most part an acquired taste. The eye has to be educated to see. How much of beauty the eye misses for lack of training! “Having eyes, they see not.” Even the most highly trained mathematician must remain unmoved by much of the splendor because it is hidden from his keenest sight. “I can’t see much in your scenery here,” said an American tourist to a guide in Wordsworth’s country. “Don’t you wish you could, sir?” was the apt retort.