Product Description

What do the Parthenon in Greece, crosses in graveyards, the ratio of the height of the navel to a woman's total height, sunflowers and Leonardo da Vinci's "Mona Lisa" have in common? The answer is that these disparate elements share a geometrical proportion of ancient origin, commonly known as the 'Golden Ratio', or expressed numerically as phi. In a captivating journey through art and architecture, botany and biology, taking in fractals and DNA on the way, Livio takes us into the heart of this extraordinary number, and gives an account of the phi-obsessed individuals who devoted their lives to discovering its secrets - from the Pythagoreans who believed that the study of the Golden Ratio would reveal the hand of God, to the great astronomer Johannes Kepler who felt that phi was the greatest treasure of geometry, to the modern day scientists who are discovering ever more remarkable ramifications of this strange, almost mystical, number. It is a journey into the heart of beauty itself.

Product Details

• Amazon Sales Rank: #285627 in Books
• Published on: 2003-08-04
• Original language: English
• Binding: Paperback
• 304 pages

About the Author
Professor Mario Livio is head scientist at the Hubble Space Telescope Institute at Johns Hopkins University, USA

Customer Reviews

Not enough interesting material on the subject.
I'd heard about the golden ratio from TV programs and wanted to find out more, in particular about the aspects related to beauty and proportion. However, much of the start of the book seemed to be spent discussing where this number may or may not have first been discovered, and in disproving a number of theories about who may or may not have been aware of it. I didn't find this very interesting, though the background on the history of mathematics might be of general interest.

The more factual bits of the book were more engaging, but it didn't really seem to have any new material or go into a huge amount of depth. There wasn't anything that had a real punch, and at the end I felt there were still a lot of questions unanswered.

So much for a little number
A very engaging work, which held my attention throughout. The so-called Golden Ratio is expressed as that ratio demonstrated by the point on a line, where the ratio of the larger division to the smaller division is the same as the ratio of the entire length of the line to the larger division. The ratio finds itself manifested in pentagons and pentagrams, certain types of rectangle, and some polyhedrons. The ratio has numerous surprising qualities and is reflected in growth patterns discovered amongst plants and animals. Livio patiently and intriguingly describes all of these patterns with evidence and is guarded against finding the ratio expressed in ancient or early art, but also traces the use of the ratio in modern art. Whilst Livio points to the inherent beauty of the numerical relationship, he finds no evidence of a particular aesthetic beauty displayed by the ratio. Livio’s discussion of the Fibonacci sequence and its relationship to the ratio is an education. The glories of mathematics can be glimpsed in this enchanting book.

Tremendous
A number of disciplines are intertwined and addressed by this riveting work, and the author's depth and breadth of knowledge in each of them is formidable yet naturally conveyed. Artists, scientists, and generalists alike will find this book hard to put down. Turning onto each new page, one wonders with enthusiasm and amazement, "where will phi turn up next?"