The Divine Proportion: A Study in Mathematical Beauty

by Ernie Hart

Using simple mathematical formulas, most as basic as Pythagoras's theorem and requiring only a very limited knowledge of mathematics, Professor Huntley explores the fascinating relationship between geometry and aesthetics. Poetry, patterns like Pascal's triangle, philosophy, psychology, music, and dozens of simple mathematical figures are enlisted to show that the "divine proportion" or "golden ratio" is a feature of geometry and analysis which awakes answering echoes in the human psyche. When we judge a work of art aesthetically satisfying, according to his formulation, we are making it conform to a pattern whose outline is laid down in simple geometrical figures; and it is the analysis of these figures which forms the core of Professor Huntley's book.
For the philosopher, scientist, poet, art historian, music listener, artist, as well as the general reader who wants to understand more about the fascinating properties of numbers, this is a beautifully written, exciting account of the search for a naturally manifested aesthetic that has occupied man since he first asked the question "why?"
"This is a delightful book to read. . . . It wanders here and there through some of the most attractive byways of simple mathematics, returning always to the oddities and pleasures of the golden section. 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." — Dr. J. Bronowski, The Salk Institute.

Genres: Mathematics, Science, Nonfiction, Philosophy, Art, Design

208 pages, Paperback

First published January 1, 1970

About the author

Also wrote under the pen-name H.E. Huntley.

American comic-book writer and artist best known for creating Marvel Comics' funny animal character Super Rabbit as well as co-creating the superhero The Wasp.

Reviews

[A.J. McMahon · Rating 5 out of 5]

This book is an investigation into beauty with special reference to the irrational number phi, which was called by Kepler the divine proportion, hence the title of the book. I should confess a personal bias at this point as H. E. Huntley was my maternal grandfather (he had two daughters, Rosemary and Alison; Rosemary was my mother). I only met him twice as a boy as we lived on different continents but I read his unpublished memoirs later on in which he spoke of one of his earliest memories: an uncle had placed a coiled wood-shaving next to his cot and he was transfixed by the beauty of this object. Beauty became a fixed interest for him later in life and this book represents the culmination of a lifetime's meditation on this topic. He was a devout Christian who decided that God had placed beauty in the world as a lure for humanity to seek the divine but at the same time he was a Professor of Physics who had to reconcile faith and science. Some reviewers have commented that the mathematics of this book is too hard for the non-mathematical reader and I must admit that I can't follow all of the mathematical argumentation either. I take more after literature than mathematics myself (having just published my debut novel, The Last Suitor, by A. J. McMahon). However, you don't have to understand every detail of the maths in order to understand the significance which Prof Huntley attributes to the divine proportion. His central goal throughout is to try to understand something of the nature of beauty and why we respond to it. In this sense his book is as accessible to non-mathematicians as to mathematicians. This book is for everyone.

[Christine Cordula Dantas · Rating 5 out of 5]

A book written with deep passion, alongside an equally profound, rational exposition on the theme of mathematical beauty. Enjoyable, clear— a fascinating book not only for interested readers, but also for those who just wish to gain a sense of aesthetic appreciation in mathematics. An amazing selection of detailed examples is presented, including examples found in Nature. Those who are able to follow the mathematical details will gain a sense of vertigo on the profound connections between the golden section and Fibonacci sequence. I highly recommend this book, whatever the reader's mathematical knowledge. It is particularly great for young students, and mathematical olympiad contestants at the adequate level. Even those who can't follow the mathematical details will enjoy the contents at some level. 5/5 stars.

[Rob · Rating 4 out of 5]

Eventually I settled in to Huntley’s style
But it was rough going, for awhile.

There is a sort of irony in reading about beauty in mathematics, when the book’s filled with stylistic zingers like these:

"Many of our appetites have been developed in the course of human evolution for a utilitarian purpose in the material environment of our mundane existence."

…

"We must accordingly conclude that the personal unconscious, as well as the collective unconscious, is the arena of the emotions as well as the storehouse of emotive memory complexes."

…

"Let us now turn from general considerations to the particular case of the emotion generated by the interaction between an object of beauty and an observer—the aesthetic feeling. If the foregoing sketch of a working hypothesis is on the right lines, then the aesthetic experience consists in the levitation from the unconscious to the surface mind of a memory complex activated by an association mechanism sequential to the visual or aural contemplation of the beautiful object. It is not difficult to guess the nature of these hidden memory complexes: they arise from the immemorial terrestrial environment of man."

Poetry, no? No. In any case, at some point I just started hearing him in the voice of Professor Frink, and he became much easier to follow: "It should be obvious to even the most dim-witted individual who holds an advanced degree in hyperbolic topology...." Haha, same guy, right?

The math was just about right for me. Not so difficult that I couldn't follow it, usually, but in quite a few cases more involved than I could immediately grasp. I would have had to break out a piece of paper and a pencil and actually worked it through myself, which I am confident I could have done. But in most such cases, I just continued on.

Huntley makes the case for beauty in math quite clear. If you are interested in the question of the usefulness of mathematical beauty in theoretical physics, well, that's not so certain. Read Sabine Hossenfelder's Lost in Math.

Oh, also, there is simply no way that this was written by "Ernie Hart." If you Google H.E. Huntley you get a hit for the Wikipedia page of Ernie Hart, who it is said wrote under the pseudonym of H.E. Huntley. Hart was an American who worked in the comics genre. However, the H.E. Huntley who authored The Divine Proportion was a brit who attended the University of Bristol and taught university-level math and physics for 30 years.

[Alex Weinle · Rating 4 out of 5]

Huntley's review of beauty in mathematics suffers a little from his tremendously stuffy tone and repetitious, near identical quotations. That being said this is a great investigation and what he fails to provide in literary inspiration he more than makes up for in examples of the recurrence of themes of phi.

You'll never look at a piece of A4 paper in the same light again.

[Esteban del Mal · Rating 3 out of 5]

A rationalist's wet dream.

[John Reis · Rating 5 out of 5]

A very interesting look at mathematics and beauty

[Michael · Rating 2 out of 5]

I'm giving this book two stars even though I was unable to finish it (which would usually mean a one-star rating), because I genuinely enjoyed the part I was able to understand. Somewhere in the middle, the math got too complex for me to follow, and I had to give up. I suspect that, if I read this book in connection with a class and with a teacher that was going through the concepts, I would have been able to finish, but it would have been taxing.

In that sense, I’m sorry to say, the author failed to achieve what he intended. He claims that an attentive reader with minimal mathematical training should be able to follow all the way through, although not without effort. I made the effort and nonetheless was unable to.

The book is written as a celebration of “Phi,” the irrational number that produces the “golden ratio” of the Greeks, and which is represented in the fibonacci sequence and myriad aesthetic constructs in art and nature. The introduction is a loving homage to mathematics and mathematical aesthetics. It is also crucial to the design of a properly-proportioned pentagram, which is at least partial explanation of how this book has found itself on occult reading lists. The author does have a bit of a spiritual agenda, as he acknowledges in the introduction, although it is doubtful whether he would agree with those of some of the groups which have adopted his work. I would say that, if you enjoy the intersection between philosophy, science, and nature, this book is worth a try, although you may find as I did that it gets to be a bit much.

[J Campbell · Rating 3 out of 5]

Interesting book, though the great pains used to develop phi in many of the examples feels a bit contrived. Reading this did reveal how weak my geometric education has been. I had to look up a lot of the geometric proofs used by the author.

[Wendy · Rating 4 out of 5]

Reminded me of why I love math so much. Beautiful, beautiful introduction.

[TRXTRMXTR · Rating 3 out of 5]

While the majority of the "proofs" in this book are beyond my grasp of mathematical concepts, the dicussion between aesthetics and math is quite interesting.

[Sue Seibert]

Still reading, fascinating so far...

[david · Rating 4 out of 5]

want to give it a three because there are a handful of not so not preposterous implications and assumptions the author makes. they are tiring. but the book is still good. insightful.

[David Cohen · Rating 5 out of 5]

A little too awed and not enough inspiring. I get that these proportions follow art, science, and are the bases for various sequences and series, but too much.

[Paul Brooks · Rating 4 out of 5]

a little math for the beginner and definitely a must for the serious student.