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The Golden Ratio: The Story of Phi, the Extraordinary Number of Nature, Art and Beauty [Hardcover]

Mario Livio
4.0 out of 5 stars  See all reviews (9 customer reviews)

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Book Description

28 Oct 2002
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 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 their 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.


Product details

  • Hardcover: 288 pages
  • Publisher: Headline Review; First Edition edition (28 Oct 2002)
  • Language: English
  • ISBN-10: 0747249873
  • ISBN-13: 978-0747249870
  • Product Dimensions: 21.8 x 14.4 x 3 cm
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Bestsellers Rank: 712,092 in Books (See Top 100 in Books)

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Product Description

About the Author

Professor Mario Livio is head scientist at the Hubble Space Telescope Institute at Johns Hopkins University, USA --This text refers to an out of print or unavailable edition of this title.

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Customer Reviews

Most Helpful Customer Reviews
19 of 19 people found the following review helpful
3.0 out of 5 stars Not enough interesting material on the subject. 31 Mar 2003
By A Customer
Format:Hardcover|Verified Purchase
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.
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12 of 12 people found the following review helpful
5.0 out of 5 stars So much for a little number 12 Feb 2003
By A Customer
Format:Hardcover
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.
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15 of 16 people found the following review helpful
5.0 out of 5 stars Tremendous 4 Feb 2004
Format:Paperback
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?"
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7 of 8 people found the following review helpful
5.0 out of 5 stars Golden Indeed! 23 Jan 2004
Format:Paperback
Following in the steps of his earlier, just as fascinating account linking cosmology and the arts ("The Accelerating Universe"), Mario Livio continues to prove he is one of the most original, exciting and literate writers of popular science today. "The Golden Ratio" is a witty and learned journey generally following the trail of the number Phi, but stopping along the way to take in subjects as diverse as philosophy, history, art, religion, the sciences, architecture, etc.
Writing about science in a way that is both knowledgeable and understandable for the common reader is an infamous hurdle, but Livio leaps over it with the greatest of ease, giving clear explanations of every potentially difficult matter and providing the scientific proofs in the appendices, for those more mathematically inclined. Overall, though, it is the great humanity of Livio's worldview that shines through the book and makes it, at least for me, one of the most memorable reads of the year.
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5.0 out of 5 stars The Golden Ratio Mario Livio 8 Nov 2013
Format:Paperback|Verified Purchase
This book is broad ranging and written in an accessible way. I have not yet finished it but am really enjoying it. I like the way he integrates history with mathematics. I would recommend it to anyone interested in the concept of phi.
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