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The Golden Ratio: The Story of PHI, the World's Most Astonishing Number [Paperback]

Mario Livio (Author)
4.0 out of 5 stars  See all reviews (43 customer reviews)
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Book Description

Release Date: Sep 23 2003
Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!

The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.


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From Publishers Weekly

Most readers will have at least dim memories from geometry class of the irrational number pi. Theoretical astrophysicist Livio gives pi's overlooked cousin phi its due with this lively account, the first on the subject written for the layperson. Phi is the golden ratio of antiquity (1.6180339887), a never-ending number so lauded for its harmonious qualities that in the 16th century it was dubbed the divine proportion. It is related to phenomena as diverse as the petal arrangements of roses, the breeding patterns of rabbits and the shape of our galaxy. Phi is also claimed to have been crucial in the design of the Great Pyramids, the composition of the Mona Lisa and the construction of Stradivarius violins. Livio (The Accelerating Universe) carefully investigates these and other claims and does not hesitate to debunk myths perpetuated by overzealous enthusiasts he calls "Golden Numberists." This is an engaging history of mathematics as well, addressing such perennial questions as the geometric basis of aesthetic pleasure and the nature of mathematical objects. Useful diagrams and handsome illustrations of works under discussion are amply provided. Livio is gifted with an accessible, entertaining style: one typical chapter bounds within five pages from an extended discourse on prime numbers to a clever Oscar Wilde quote about beauty to an amusing anecdote about Samuel Beckett and finally to an eminently clear explanation of G"del's incompleteness theorem. With a guide to the history of ideas as impassioned as Livio, even the math-phobic can experience the shock and pleasure of scientific discovery. This thoroughly enjoyable work vividly demonstrates to the general reader that, as Galileo put it, the universe is, indeed, written in the language of mathematics.
Copyright 2002 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.

From School Library Journal

Adult/High School-Take something as simple as a line segment and mark it at just the right place. Looking at it with a mathematician's eye, an interesting relationship appears: the ratio between the whole line and the larger of the pieces it was broken into is the same as the ratio of the larger piece and smaller piece. Better known as "the golden ratio" or phi, 1.618- is a number that has fascinated humans for several hundred years, and people have claimed evidence of phi in all manner of things. Livio takes readers on a treasure hunt for phi from ancient times through the present. On the way, he debunks a number of popular myths (e.g., the notion that Mondrian used it in his abstract paintings) and does a wonderful job explaining the Fibonacci sequence and its relationship to phi. Small, black-and-white photos and reproductions demonstrate items mentioned in the text. While it may seem that the author wanders in his expositions, his excursions into history and number games add fun and depth for those who wish to follow. To get the most out of The Golden Ratio, it is best to have an understanding of algebra and basic trigonometry, although the book is great for general readers who don't mind working a little to gain a lot of understanding.
Sheila Shoup, Fairfax County Public Library, VA
Copyright 2003 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.
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Inside This Book (Learn More)
First Sentence
The famous British physicist Lord Kelvin (William Thomson; 1824-1907), after whom the degrees in the absolute temperature scale are named, once said in a lecture: "When you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind." Read the first page
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Customer Reviews

Most helpful customer reviews
6 of 7 people found the following review helpful
5.0 out of 5 stars Excellent overview of the significant number Mar 18 2004
By Vladimir Miletic
Format:Paperback
OK, I don't come across PHI as often as I come across e or pi. This book was nevertheless a fascinating read, even though (as one of the reviewers pointed out) Livio tries to talik about math and applications which can seem somewhat tedious at times.
The books deserves five stars for the following things:
1. It's very well written (I read it in an afternoon)
2. It's informative and not too 'scientific' - you can understand it even if you're not good with numbers at all.
3. It's realistic - most books about this topic tend to be more fantasy than reality. Mario Livio has made sure that he debunks myths and relies only on well checked facts.

- If you like popular science books don't miss this one, it's well worth your time.

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2 of 3 people found the following review helpful
1.0 out of 5 stars More like the Golden Bore Mar 15 2004
By Thomas Paul
Format:Paperback
What a depressing book this turned out to be. I thought a book about the "golden section" would have been interesting but in the hands of Mario Livio it is pure pain. To give a few examples... The author discusses the theory that the golden ratio was used by the builders of the pyramids and refutes it easily. And then continues to refute it for page after page. Then he does the same thing with the Parthenon, destroying the theory using the exact same reasons he used for the pyramid, explaining them in the same level of detail. But he isn't done yet. We get to have the same discussion again when we look at Renaissance paintings. I didn't really care about the discussion when discussing the pyramids but by the time I heard the argument for the third time I was ready to find something else to read. As he discusses the history of the golden section he goes into side trips to discuss anyone who had even the slightest relationship with phi. Anyone who has never heard of Kepler may find this interesting even if it is irrelevant to phi but I just started skimming pages hoping for something a little meatier. There is a little spark here and there that kept me reading hoping for more but more never arrived. A writer with a greater interest in the mathematics of phi could have made this a fun and interesting book. Livio seems to think the math is boring so he avoids it like the plague and creates a book that completely misses the point and ends up being a total bore.
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4.0 out of 5 stars The Golden Ratio: A Critical View Jan 16 2009
By Lee Dale
Format:Paperback
A critical view of Phi, tracing mathematics from the pyramids to now. Particular attention is paid to Fibonacci numbers and Phi, both in natural occurrences such as patterns in the universe, plant life, and more, as well as man made occurrences.

Funny that watching Numb3rs: Season 1 after reading this book destroyed the credibility of the math referenced in the show when the lead character mentioned The Golden Ratio being used in the Pyramids.
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Most recent customer reviews
5.0 out of 5 stars A Difficult Mathematical Concept Revealed
As a non-mathematician I appreciate any help I can get in understanding the more esoteric parts of math. The Golden Ratio is just such a concept. Read more
Published on July 2 2004 by David B Richman
4.0 out of 5 stars A great guide to an amazing number
Livio's book is really an interesting look at a number similar to pi in that's an irrational number which displays itself in various places in nature, from the arrangement of... Read more
Published on Jun 21 2004 by Brian
5.0 out of 5 stars Mathematically Profound
Broad streams of literary, historical, aethsetic and religious thought are pooled together in a concise and well-illustrated review of this powerful proportion, which recurs in the... Read more
Published on May 21 2004 by Thomas J. Shelford
3.0 out of 5 stars Uninspired philosophy of mathematics
The book seems to have two purposes. First, it seeks to debunk the notion that the 'golden mean' is intuitively pleasing to all humans. Read more
Published on Mar 29 2004 by Mark Mills
1.0 out of 5 stars Predictably Prejudiced
The big problem with this book is it seems to exist only to debunk. It tends to debunk in a Matrin Gardner-ish manner, by stating only some of the facts about a subject, then... Read more
Published on Mar 27 2004 by Eugene Nielsen
5.0 out of 5 stars Best book I've read on the subject!
Without a doubt, The Golden Ratio is the definitive book on the subject of Phi, and one of the best popular science/math books ever.
Published on Mar 2 2004
1.0 out of 5 stars Fill the books with words but not with content
I bought this book expecting to learn something about phi (mathematically). But it is not up to par. Read more
Published on Feb 22 2004 by rhw001
3.0 out of 5 stars Not quite what you might expect
Bought this after reading Da Vinci Code, and I was looking for more of the same. it is a little dry. It is a quick read though, and how much do you want to know about 1.618?
Published on Feb 10 2004 by Scott Clarey
1.0 out of 5 stars I'm not a mathematician, but I find this book shallow.
This is one of the lightest pieces of fluff that I have read in a while. With holes in Livio's arguments and almost no serious analysis, this book is not for any reader who has... Read more
Published on Jan 30 2004
4.0 out of 5 stars Two books in one; one pretty good, one tedious
This book, as its name suggests, is about an interesting number, the golden ratio (which I prefer to call "tau," but the author usually refers to as "phi,"... Read more
Published on Jan 14 2004 by Bruce R. Gilson
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