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

Mario Livio
3.9 out of 5 stars  See all reviews (45 customer reviews)

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Product Description

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.

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.

Product Details


Customer Reviews

Most helpful customer reviews
7 of 8 people found the following review helpful
5.0 out of 5 stars Excellent overview of the significant number March 18 2004
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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1 of 1 people found the following review helpful
5.0 out of 5 stars Mathematically Profound May 21 2004
Format:Paperback
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 natural world in surprising places both large and small. Clearly presented mathematical proofs give the book a solid backbone. Mathematical ideas are expressed in the book through a combination of prose, appendix proofs, and plentiful illustrations & diagrams. This allows readers of varying mathematical ability and learning styles to appreciate the beautiful ideas that Livio gracefully presents. A must for serious lovers of proportion & geometry, architects, mystics, painters, graphic designers and mathematicians.
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1 of 1 people found the following review helpful
4.0 out of 5 stars A great guide to an amazing number June 20 2004
By Brian
Format:Paperback
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 petals on a flower to the logarithmic spirals of galaxies.
Livio explains the original formulation of this number by Euclid and proceeds to address the various times in history in which it may have been employed by architects, artists and musicians.
I think this is a really good book if you're interested in reading about the most "irrational of all irrational numbers".
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5.0 out of 5 stars A Difficult Mathematical Concept Revealed July 1 2004
Format:Paperback
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. Fortunately, Mario Livio has shown much light on this remarkable corner of geometry in his book "The Golden Ratio."
It is little wonder that such numbers as the Golden Ratio were considered magical. The never ending, never repeating number that cannot ever be expressed as a fraction has an uncanny tendency to show up in the oddest places, not only galactic structure and nautilus shells, but in plant parts and composition of paintings and music. Unfortunately magical numerology can lead to far-fetched relationships, as to the so-called number of the beast (666), and to academicism in art. Just because the Golden Ratio results in a pleasing relationship in a composition we are not tied to always measure art on how well it fits that ratio!
Livio has illuminated the history of the Golden Ratio in such a way that much of the associated themes can be understood by the reasonably educated laymen. While some of the book can be tough sledding for most of us non-mathematicians, the gist is available to all with some effort.
Read this book to learn about the history of interpretation and misinterpretation of mathematical concepts.
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3.0 out of 5 stars Uninspired philosophy of mathematics March 29 2004
Format:Paperback
The book seems to have two purposes. First, it seeks to debunk the notion that the 'golden mean' is intuitively pleasing to all humans. Secondly, the book argues that we can best understand the cosmic meaning of life via numbers. From these two theses, the author establishes the 'genius' mathematician as mediator and priest between mankind and the cosmos.
Ok, enough mumbo-jumbo. If the above interests you, read the last chapter first. It should have been used as the introduction and will clarify the purpose of arguments presented throughout the book.
Getting back to the book's narrative, the early sections seek to debunk various claims that Egyptian and Mesopotamian civilization use the Fibonacci ratio. Reports of its use in China are ignored. Later, there is a section debunking the notion that great art 'uses' the Golden Mean. Scattered throughout are developments in number theory, starting with Pythagoras and continuing with the standard European mathematical genius roll call. The last chapters reveal the relationship between the Golden Mean and complexity/chaos theory/fuzzy logic/quantum theory/etc.
Livio's Fibonacci sequence, Penrose tilings, and quasi-crystals stories will probably engage the recreational mathematicians among us, and provide a handy 'all in one place' summary of such matters. Others will find the philosophic overtones tangential and/or distracting. Any successful philosophy of math needs to address the issues of cardinality and ordinality at the level of intuition. The two topics are dismissed by page 15, but they underlie the whole issue of 'intuitive acceptance of number theory'.
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4.0 out of 5 stars Two books in one; one pretty good, one tedious Jan. 14 2004
Format:Paperback
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," though explaining the reason for both symbols). For those who do not know what this number is, it can be defined in many ways, but the simplest is as the number which, when it is squared, is increased by 1. The fact that all the other definitions gives the same number is the reason for its great interest among recreational mathematics fans.
The biggest problem with this book is that it tries to do two different things. One of the "two books" that I see in this one is about the _mathematical_ properties of the golden ratio. And this part of the book covers a lot of ground, and as a result I like it very much, as one of the few recreational math books I've seen recently that is easy to read yet still teaches me something I didn't know before I read it. The other part, however, is simply a refutation of claims made by many people that this or that artist consciously employed the golden ratio in his work. And it's interesting at first, but becomes tedious as he marshals more and more evidence refuting these claims. If the book confined itself to a discussion of the mathematical properties of the golden section (which is intimately related to such things as the Fibonacci sequence, Penrose tilings, and quasi-crystals), it would have merited 5 stars from me. But the attempt to refute all the artistic claims causes it to bog down for me, and causes me to cut one star off.
One thing that totally puzzles me is his terminological decision to use "phi" rather than "tau.
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Most recent customer reviews
5.0 out of 5 stars Five Stars
Excellent as usual from Mario Livio
Published 2 months ago by Pedro
2.0 out of 5 stars Golden Ratio is Astonishing, Magic, Wondrous; for those who care
Do you get excited upon discovering properties of mathematic topics? If the answer is a resounding “yes”, then The Golden Ratio: The Story of Phi, the World’s Most Astonishing... Read more
Published 5 months ago by Marissa
4.0 out of 5 stars The Golden Ratio: A Critical View
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... Read more
Published on Jan. 16 2009 by Lee Dale
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 March 27 2004 by Eugene Nielsen
1.0 out of 5 stars More like the Golden Bore
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. Read more
Published on March 15 2004 by Thomas Paul
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 March 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
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