Divine Proportion: Phi In Art, Nature, and Science

by Priya Hemenway

The number Phi, simply defined, is one plus the square root of five, all divided by two. But its myriad occurrences in art, nature, and science have been a source of speculation and wonder for thousands of years. Divine Proportion draws upon both religion and science to tell the story of Phi and to explore its manifestations in such diverse places as the structure of the inner ear, the spiral of a hurricane, the majesty of the Parthenon, and the elusive perfection of the Mona Lisa . A universal key to harmony, regeneration, and balance, Phi is at the heart of a tantalizing story begun on clay tablets in ancient Babylon, and which will continue to be written for centuries to come.

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

208 pages, Hardcover

First published January 1, 2005

Reviews

[Michael Snuffin · Rating 4 out of 5]

I knew little bits here and there about the import of the Divine Proportion, but The Secret Code puts everything together in one package. This does not read like a mathematical text; The Secret Code appeals to a more general audience, moving beyond the strictly mathematical import into connections with science, art and nature. The book has over 300 illustrations to assist the reader in grasping the whole concept of the Divine Proportion--the main purpose of this book.

I found the information on Fibonacci most interesting. Many people know about the numerical sequence named after him, but he actually made much more important contributions to mathematics. He introduced the Hindu concepts of number symbols, place values, and zero to the Western world in the 13th Century. Previously, they used Roman numeral and abaci to calculate numbers. This made multiplication and division very complicated! Needless to say, eventual acceptance of these new concepts revolutionized accounting and other business operations, not to mention Western mathematics.

The Secret Code also reminded me that Ptolemy's geocentric model of the universe stood for almost 1500 years until Copernicus proposed his heliocentric model in the 16th Century. It blows my mind that we only figured this out 500 years ago! Yet another example of religious ignorance impeding science.

I do have one primary criticism of the book. It appears obvious that someone (writer or editor) padded or fluffed-up the original manuscript. The connection between some of the images and the text seems tenuous at times. The content of the final chapter of the book had almost no relevance to the subject, and its deletion would have improved the book immensely. The book ends on a weak note.

One other thing: Some marketing genius decided to make the dust jacket of this book out of vellum (or something like it), and the dust jacket does not like to stay on the book. They wrap the book in plastic to hide this fact. Don't let that deter you from buying the book though. If you desire a good introduction to the Divine Proportion, you will not be disappointed with The Secret Code.

[Alina Cristea · Rating 4 out of 5]

Interesting history of the golden ratio and its occurrence in various domains.

[Emile Antoine · Rating 5 out of 5]

Perfect combination of mathematics, history and philosophy. How beautiful and fulfilling to read about a universal principle that describes a harmonious relationship between the microcosm and the macrocosm.

[Alejandro Melo-Florián · Rating 5 out of 5]

El propio conocimiento puede llegar a partir de conocimiento del universo, y al conocimiento del Universo se llega en la medida de conocer este número o sección aúrica o divina proporción (cada uno de los autores y estudiosos importantes desde Euclides hasta Fibonacci (Leonardus Pisanus, 1170 – 1250), pasando por Luca Paccioli (1445 – 1517) y Leonardo Da Vinci le han dejado su impronta en el nombre) que tiene “la propiedad única de generar armonía, regeneración,equilibrio por la facultad única de conectar las partes de un conjunto de tal forma que respeta sus propiedades individuales al tiempo que permite generar un patrón mayor de un único conjunto“.
Pues resulta que un cosmólogo francés de nombre Jean Pierre Luminet describe que el universo puede tener forma de dodecaedro!, con distancia de 30.000 millones de años luz…..Y en muchas obras que todavía perduran, el número aúrico formó parte de planeación: la catedral de Notre Dame, la de Chartres.

Todo esto es para destacar que los puentes entre misticismo y astrofísica -aunque suene raro-, están pasando por el mundo de las matemáticas.

Un detalle para resaltar: es profusamente ilustrado, los conceptos se entienden mucho mejor.

[-uht! · Rating 2 out of 5]

Fun intro to Phi. Not very deep, but it provides a decent smattering of ideas about phi. There was some cursory discussion about sacred geometry, too. The most interesting parts were the discussions of the Greeks and how they were trying to find meaning in the world through its structure. Geomerty became tantamount to religion and the divine. I think some people are still doing this, but for the most part, the *how* is a mechanical search and people have divided into two completely separate camps.

Anyway, there's a lot more detailed information about Phi here: http://goldennumber.net/. It's a really fascinating natural phenomenon and I hope to encounter a book that will tie it to science at some point.

[Cheryl Gould · Rating 5 out of 5]

Fascinating look at the coincidences or the design of our world through mathematics - specifically Pi and the Fibonacci sequence and the resulting "Golden Section". The book looks at how the worlds of art, science and living things are governed by or can be explained by ratios. Lots of historical pictures. When I first started reading it, I just read a few pages and put it down enjoying a bit of scientific history. By the middle of the book, I got really fascinated by the point of the book. Can everything really be explained by 1.6180339...?

[Jacob · Rating 5 out of 5]

the most interesting thing i learned from this book was how quantifiable beauty is. something that we think is so qualitative or subjective is really defined by a few sets of proportional values that has been understood for thousands of years. also, aristotle discovered not only that the universe has a shape, but what that shape is.

[Glamdring]

*Review to come*

[Jennifer · Rating 5 out of 5]

I read the entire thing in two sittings, and said "wow..." out loud several times. It's amazing how the world fits together.

[Carolina Álvarez Valencia · Rating 4 out of 5]

Una ventana a una interconexión de temas proclives a ser profundizados. Lectura muy entretenida.

[Humphrey J · Rating 3 out of 5]

I bought this book several years ago from the British Museum whilst visiting and unfortunately neglected it until recently.
I certainly wish I had read this earlier- the information it provides on the history and (interpreted) meaning of the "Golden Ratio" is invaluable.
However, the book is by no means perfect. The author evidently believes in the spiritual power of "phi" (a passion that bleeds well into the writing), which results in them glossing over some of the critiques of certain purported instances of "phi" (I.e. the Parthenon, Great Pyramid and Fechner's study).
However, this lack of sceptical perspectives by no means hinders this book, so long as you maintain a sense of critical reflexivity, and serves as an excellent prompt for your exploration of the "Golden Ratio".

[John · Rating 5 out of 5]

A beautifully crafted book with high-quality illustrations that presents an extraordinary, even mystical topic in a well-balanced and accessible way. The Hemenway explains the history and significance Golden ratio (and its many other names). Geometry is a way of unlocking and understanding the universe. Triangles, Pythagorean Theorum, and the Golden ration make one believe there is something inexplicable behind the universe. Galaxies, the human body, hurricane, the Nautilis, flowers, and DNA spirals are connected through the golden ratio. One can't help but think about the mystery and beauty behind this geometry. Maybe the best book I've read in 2019.

[Gerry.Aki · Rating 5 out of 5]

An excellent, fantastic guide to sacred geometry, that can either be used as an appealing introduction to the topic or a nice-to-look-at reference guide. I highly recommend. All ideas from how the Fibonacci code is used in music, the natural world and art, ect, are explained simply and are accessible to everyone.

So who can enjoy this book?
I recommended this to a friend who said that she was not good at maths so wouldn’t be able to understand it; if you feel the same way then don’t be put off! All you need to know is how to add numbers. Besides, it’s more humanitarian than mathematical.

[Conchi · Rating 3 out of 5]

Es un buen libro para recordar lo divertidas que son las mátemáticas y el estudio de la naturaleza. La base más fundamental de las ciencias, la curiosidad, es central en todo el libro, tanto mostrandote datos curiosos de estudiosos antiguos como mostrando conexiones entre ramas del conocimiento, historia, arte, sociología, psicología... me ha chirriado a ratos cierta mitificación de la ciencia, entendiendose mitificación como crear toda una narrativa de idealizar y contar en tono de épica el trabajo de muchas personas a lo largo de los siglos, y también cierta mística, pero no de la interesante, no de la conexión que muchas personas han sentido entre el estudio científico y lo espiritual, que es lo que a mí me llama, sino una mística de entender a los científicos como seres que no comprendemos... existe el mismo prototipo de artista y siempre me ha chirriado, pq le quita una humanidad que a mi parecer hace todo mucho más potente. Igualmente, he aprendido mucho y es muy disfrutable. Ahora veo el número aureo en todas partes

[Alexander · Rating 4 out of 5]

This book is heavy-laden with information relating mathematics, art and science. Nonetheless, it is an interesting read, which is best approached at a slow pace. I wouldn't recommend speeding through this book because each few pages have a substantial amount of information that takes time to mentally digest. The author clearly demonstrates a diligent effort to support her information with a proper amount of research, historical context and beautiful images.
In this book we learn to perceive nature within a mathematical framework, and we observe how humans have been following nature's example of beauty and practicality for millenia. "The divine proportion," which represented by the greek letter, "phi," truly denotes a sacred concept, a concept of which one can meditate upon for a lifetime.

[Artur Coelho · Rating 4 out of 5]

É um dos padrões matemáticos clássicos, que desde a antiguidade tem sido considerado uma fonte de beleza e mistério. A proporção dourada é o ponto de cruzamento entre matemática, geometria, misticismo e história de arte. O fascínio com este padrão tem sido uma constante, entre as suas manifestações naturais ou o seu uso na arte e arquitetura. Das romãs ao Parténon, das tesselações matemáticas à arte renascentista, o Phi e a proporção dourada têm fascinado artistas, filósofos, matemáticos e conhecedores de arte, naquele sentido classicista de elemento com o seu quê de mistério. Este livro traça um panorama histórico do Phi através das eras, profusamente ilustrado para nos mostrar a sua influência estética. É uma daquelas obras que os apreciadores de arte apreciam, pelo conteúdo, e pelas reminiscências que traz.

[Cem Yüksel · Rating 3 out of 5]

History of divine proportion or golden section with its reflections on nature, science, architecture and beliefs. Rich with illustrations (sometimes a bit irrelevant for the subject on the page) , people in the history from Euclid, Ptyhagor to Hayyam, Rumi, Keppler, Fibonacci, Leonardo and many other. Nice one for the people interested in the subject although some chapters have some parts which are a bit out of the subject’s framework.

[Paul De Belder · Rating 2 out of 5]

Erg slecht boek, mede door de incompetentie van de vertaler. Heel veel fouten en onzin, als mystiek gepresenteerde, onbegrijpelijke woordenbrij en niet onderbouwde speculaties over de gulden snede. Elke uitspraak in oude geschriften over verhoudingen of harmonie worden aan de gulden snede gekoppeld. Wilde speculaties over bv. Egyptische mystiek en “wijsheid”, waarvan geen enkel spoor is teruggevonden. Je leest beter “The Golden Ratio” van Mario Livio.

[Unnamable · Rating 1 out of 5]

The idea of the book is excellent, but its fulfilment is disappointing: the layout of the text and the images is very confusing. There are parts where the main text “disappears” to some other page while the reader is still trying to catch up with the descriptions of the images, etc. This makes the whole reading experience quite complicated.

[Richard Marney · Rating 5 out of 5]

An enjoyable journey through the history of this “ divine proportion” for readers ranging from the gardener observing apparently inscrutable patterns in their flower gardens to advanced mathematicians applying their science to our complex world of technology, industry, commerce and finance. The pictures are beautiful. This is a wonderful book!!! 😀😀

[silly goose · Rating 4 out of 5]

Can I say that this is an obligatory book to have for those of us, who are interested in design? It is a perfect visual and not only, guide for the technical drawing as well as an easy introduction to geometry (of course, for those who forgot or never studied it).

[M. · Rating 5 out of 5]

Un libro que no solo nos muestra la matemática detrás de esta fórmula mágica. Las imágenes con su correcta investigación sobre religión, naturaleza y arte hacen que este libro se disfrute sin lugar a dudas.

[Stijn Creten · Rating 3 out of 5]

Deels interessant, deels overbodig. Had sowieso ‘iets anders’ verwacht inhoudelijk, een meer praktische benadering. Laatste hoofdstuk was voor mij overbodig, of op zijn minst te vluchtig om interessant te zijn.

[Aaron the Pink Donut · Rating 3 out of 5]

A brief but enjoyably romp through the history of PHI.

[Dirk · Rating 3 out of 5]

Readable and for the moment the most accessible book on the subject I've found.

[David M · Rating 5 out of 5]

Euclid, geometry, the Golden Mean, Golden Ratio, Golden Rectangles, Golden Triangles, Golden Spirals, Fibonacci. Fascinating.

[Aimee Went · Rating 3 out of 5]

maths be wack

[Nicolas Groubos · Rating 5 out of 5]

Très pertinent tant sur le côté histoire que mathématique!

[Deryk Rumbold · Rating 3 out of 5]

Love the illustrations! Easy practical steps to draw the ratio (1+(5)^1/2)/2. Which may not come in handy very often but still cool regardless!

[La peor de todas · Rating 4 out of 5]

"Gloria, hazmerreír y enigma de este mundo"