The Divine Proportion (Paperback)

~ (Author) "Before launching out on our main topic, beauty in mathematics, it will be worth while to convince ourselves that the effort required to learn to..." (more)
Key Phrases: golden cuboid, golden series, equiangular spiral, Cross of Lorraine, Leonardo of Pisa, Liber Abaci (more...)

Editorial Reviews

Product Description

Engaging introduction to that curious feature of mathematics which provides framework for so many structures in biology, chemistry, and the arts. Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal’s triangle, the Fibonnacci series and much more.

Product Details

• Paperback: 186 pages
• Publisher: Dover Publications (June 1, 1970)
• Language: English
• ISBN-10: 0486222543
• ISBN-13: 978-0486222547
• Product Dimensions: 8.3 x 5.4 x 0.5 inches
• Shipping Weight: 8.5 ounces (View shipping rates and policies)
• Average Customer Review: 3.3 out of 5 stars  See all reviews (10 customer reviews)
• Amazon.com Sales Rank: #107,025 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

45 of 45 people found the following review helpful:

4.0 out of 5 stars Very fun book, despite a few far-fetches, September 15, 1999

By A Customer

Can one write a whole book about a number? Well this book is basically about the golden ratio ( [1 + sqrt(5)]/2 = 1.618...]), usually represented by the greek letter "phi" (and I'll refer to this number here as phi). The book gives tons of examples where phi shows up, and it does amazingly show up in places where one might never expect it. But the book isn't just a pile of examples. As the title implies, it is also about math and aesthetics. There are some interesting historical notes and art/aesthetics commentaries from the author. Huntley proposes (and I might be oversimplifying a bit here) that phi is a universal number of beauty, since it manifests itself in many aesthetically pleasing things, from patterns in nature to famous artwork and architechture. He also points out lots of purely mathematical curiosities of phi (like the connection between it and the fibonacci sequence, continued fractions, etc.)

My only complaints is that there are a few connections that seem far-fetched. Again, the book _is_ filled with plenty of amazing examples where phi shows up, including many places where one might least expect it. But really, not every sighting of "1.6" calls for a cry of "eurika"! (And oddly enought, at some point the author criticizes the ancient Greeks for once acting like that!) The section on music had some flaws and really far-fetched claims, which is too bad, since I've always loved researching the math/music connection.

But over all, the book does leave me wondering why Pi should get all the fame.

48 of 50 people found the following review helpful:

4.0 out of 5 stars Solid intro to the golden rectangle, April 4, 2000

By	"treman" (Ann Arbor, MI) - See all my reviews

This book is perfect if you enjoyed the movie Pi and want to learn more, or if you are researching connections between math and religion, art, quality (per R. Pirsig), or aesthetics. One downer is that Huntley tries, and fails, to explain how math can be beautiful just like poetry can be beautiful. I personally think that you either dig math or you don't. Huntley should assume that anyone reading his/her book is at least interested and therefore skip the "math can be pretty too" lesson. Beyond that, though, the book is a thorough introduction to phi and the golden ratio. Huntley more than makes up for his mentioned faults by providing numerous equations, proofs, plots, and diagrams. The math level is pre-calculus with emphasis on geometry. I recommend reading this with plenty of scratch paper handy so that you can work along with the text and prove to yourself how deep this rabbit hole goes.

106 of 117 people found the following review helpful:

3.0 out of 5 stars Mathematical error and misleading conclusion on page 99., August 14, 2000

By	Danni Akers (South Carolina) - See all my reviews (REAL NAME)

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For the most part an excellent, easy to follow work. However, on page 99 (item #3, bottom of page) the author states the incorrect equality: 2(phi+1+1/phi)=4, for the surface area of the golden cuboid. Correctly, the surface area of the given cuboid should be equal to approximately 6.472. This error could be overlooked except for the fact that the author extrapolates on this incorrect result (next page, item #4) and hints at a connection between pi and phi. The author uses his incorrect constant of proportionality, namely "4", which appears in the figuring of the surface area of the circumscribing sphere and the cuboid, as evidence of this "connection". Thus, in the guise of some illusive geometric "hint", leaving the reader with the idea that a tie between these two constants may exist in this geometric figure. The significance of this error cannot be overlooked.