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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

3.79  ·  Rating details ·  5,766 ratings  ·  360 reviews
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 th ...more
Paperback, 294 pages
Published September 23rd 2003 by Broadway Books (first published 2002)
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Jul 11, 2007 rated it liked it
Shelves: math_physics
When people leave organized religion, they often look for mystical awe elsewhere. Math is a not infrequent haven of new agers who gave up on the tried and true faiths of their parents. Real math takes lots of work, whereas quick mystical attachment takes very little effort.

This book shows how many people have read far too much into Phi (1.6180339887 ...) [The Golden Ratio]. The author shows how, Phi is prevalent in nature, but it is not magically so. Phi's prevalence is due simple to the nature
Apr 04, 2017 rated it liked it
Well, I was expecting something a bit more exciting because of my natural love for Phi, simply because, you know... SPIRALS are EVERYWHERE, Dude.

Still, the author does a palatable job of giving me a fairly decent history of mathematics from the focus of the Golden Ratio, the Golden Triangle, the logarithmic spiral, the Fibonacci sequence... all of which is, of course, the same thing, expressed slightly different with a ton of additional cultural significances.

No surprise here. This is Phi.

Jul 10, 2011 rated it it was ok
Shelves: romanian
so I stayed up past bedtime tonight to finish this book, not because I love this book, but because I would give anything to not be reading it anymore and now I'm not.

I'm not a platonist. I don't look at concepts made up by humans and say those describe things humans see so they must have a magical relationship to truth. I actually weirdly assume when people make things up those things should be related to what is true so it is a given they will relate to true things.

there were parts of this th
Dec 02, 2014 rated it really liked it
Livio's book examines the convoluted history and applications of phi. Like π (pi) it is both a constant and an irrational number. It's derivation is deceptively simple. Imagine a line divided into a longer segment (a) and a shorter segment (b); the dividing point is placed so that the longer segment (a) compared to the shorter segment (b) is proportional to the entire length (a+b) compared to the longer segment (a). In other words, a/b=(a+b)/a=phi.

In mathematics, there are many ways to express t
Mar 15, 2011 rated it really liked it
Here I go all math geeky again. I picked up this slim book (about 250 pages) a couple years ago and then I started thinking about it and felt compelled to read it. (Voices in my head. You know.) The golden ratio, or phi (pronounced "fee"), was first discovered by Euclid (remember him from geometry class?). Somewhere around 300 B.C. Euclid--

YOU: Whoa-whoa-whoa, wait a minute, Woodge... you actually read another book about math. For fun?! Are you for real?
WOODGE: Yeah, you TV Guide-reading eejit!
Kara Babcock
This is one of the oldest (perhaps the oldest?) physical books I own and have yet to read. Goodreads suggests I’ve had it for nearly a decade. Oops. The truth is, I was never excited to read this. I love reading math books! But I am not particularly enamoured of books that explore one or two “special numbers,” and phi is perhaps my least favourite special number. The blurb from Dan Brown on the cover didn’t help. See, phi has been egregiously sexed up and romanticized by people, turned into a my ...more
EJ Natale
May 20, 2011 rated it did not like it
Terrible book. Poorly written. Vague. No direction.

This book is more numerology. The author creates loose and thin parallels to Phi, then refutes them. This happens repeatedly throughout the book.

The great pyramids might be built based on a ratio similar to phi. Oh, no, maybe not.
Oh, these painting might contain phi built into some of the geometry. Oh, wait, nope. They don't. The artist didn't even know what phi is.
The content makes no sense.

The author goes into lengthy sidebars about art and
Aug 03, 2014 rated it really liked it
Shelves: pop-science
The Fibonacci sequence (and its consequent relationship to the Golden Ratio) is one of my favourite things. No, really. So I went into this book already interested and somewhat informed. Not sure if that would make a difference, though, because Livio's treatment of this topic is really solid. For one thing, it's clearly written -- which always helps for the artsy reader -- and while formulae and proofs litter the pages, concrete examples and pictures show up frequently. The structure of the book ...more
Sep 19, 2018 rated it did not like it
Am I nerd for voluntarily reading this? Yep.
Do I care? Nope.

I'm not the brainest person on the planet. Actually, I'm not very geeky at all. But I love to learn. I like to spend time analyzing and picking things apart ; dissecting the material and discussing it with someone. However, not everything enchanted me and this book straight up annoyed me.
Essentially, I went into this book expecting to be, I don't know, told about Phi. The discovery, the relevance, the applications and help it provided
Mikael Lind
Aug 08, 2013 rated it really liked it
A fascinating historical expose about how a single number, phi, has (or is believed to have) influenced human creation within such different fields as music, art, architecture and, of course, mathematics of different kind.

The book's strength is that you don't have to be a mathematical minded person to be able to understand it. I could follow the mathematical formulas roughly by the mathematical knowledge I gained more than fifteen years ago, but even though I was persistent enough to try to foll
Jul 28, 2013 rated it really liked it
Phi has some surprising mathematical properties, which are eventually discussed here and there throughout the book.

Mostly, this book is a history of mathematics. From the etymology of numbers, to the Pythagorean brotherhood, and the discovery of incommensurability, and finally, to modern day mathematics.

The book dispels myths of Phi's use in famous works of art, construction of the pyramids, etc.

I find Livio to be a trustworthy author, who prefers demystification over hyperbole, which I respect.
Cassandra Kay Silva
May 11, 2009 rated it it was amazing
Shelves: mathematics
I was so excited to get this book. I have a minor obsession with the golden section/ratio. I have always somewhere deep in my heart hoped that string theory would turn out to have strings vibrating at ratios or frequencies somehow related to the golden section. Unfortunantly I already knew everything in this book. Nuts~! I was hoping to get some new information. I don't think that is a fair reason to say that the book was not great. It was still really fun. ...more
Apr 01, 2009 rated it really liked it
Mathematical constants make engaging characters in the popular imagination. At least the rash of books for general audiences in this vein published in the last two decades suggests this. Astro-physicist Livio's leading character is a somewhat less well-known constant - those special numbers discovered or created by mathematicians over the centuries. Phi - the so-called Golden Ratio - has been known since Euclid. Geometrically, given a line AB cut by point C, where AC > CB, then locate C on the l ...more
May 05, 2014 rated it really liked it
This is a great book about number theory in general and is much more than just the discussion of phi, the golden ratio. It is truly amazing to see how often this number and ratio are found in nature. The widths of the spirals of pinecones and various flowers display the ratio as due patterns in the breeding of rabbits. But some of the numerical properties of the number are equally fascinating. For instance 1/phi is equal to 1 + phi. There is also a section on prime numbers which is just as inter ...more
Rosemary Paul
Jan 11, 2013 rated it it was amazing
Shelves: engineering
It is a great book. I finished it in 2 days. Very stimulating in that I love books that try to give a relationship between numbers and the nature of reality.
PHI 1.6180, not to be confused with PI 1.14159, is considered the Golden Ratio. Discovered by Euclid over two thousand years ago.
The book 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
Christopher Litsinger
My review for this book will consist of the suggestion of a new title: "In which the author describes in great detail several ways in which the Golden Ratio was documented to be used in art and architecture and then proves those ways to be false with very little detail, and then rambles on for a bit about some other number theory and whether or not God is a mathematician, but generally leaves you somewhat less impressed with Phi than you were to begin with"
I'll admit it's not very catchy, but it
Aug 26, 2009 rated it it was amazing
This book was given to me by my daughter and son-in-law. Excellent read! I was familiar with the golden ration already from a few of the science reads I have done but this book zeros in on it 100 %. You go from the last page mesmerized by the beauty of all existence with an insurmountable awe with the connection of everything. Not even 4 years of studying philosophy can expose you to the awe of this one book.

This book is a mathematical utopia.

A must read.
Dec 19, 2015 rated it it was amazing
This was a wonderful book, full of fun thought provoking ideas on the history of knowledge and learning. Two thumbs up, five stars, highly recommended.
Jan 27, 2019 rated it it was amazing
Very good book about mathemathics and the golden ratio (1.618), a number which suprising presence and application is found in art, physics, statistics and many other areas.
May 11, 2013 rated it it was amazing
Shelves: math
Reading this book was a stimulating experience. Exploring the mathematical principles and theories studied by various past cultures and how they employed them isn't a new idea but this author is uniquely good at it. Other authors in this genre, such as Amir Aczel can sometimes be guilty of spending too much time on sculpting the biography of a math genre and leaving its concepts severely under-explained. Livio however, created what I felt to be an adequate mix between math teaching an math biogr ...more
Kyle Wright
Having expected a book filled to the brim with Phi related information, I feel let down by the end result. Livio's book covers a broad history of mathematics and geometry in general, with instances of phi thrown in where context allows. While I did learn a lot of interesting information about the origins of math, I felt that Livio left little space for the phi-related aspects, which was the primary purpose of my reading this book.

When Livio does manage to address phi directly, he does so by debu
Mar 14, 2019 rated it really liked it
This review has been hidden because it contains spoilers. To view it, click here.
Aug 03, 2011 rated it it was amazing
Mario Livio's The Golden Ratio nicely balanced the last book I read about the world's most astonishing number. Actually, it far surpassed it! While Livio debunks the opinion of others that phi is conspicuous in the ancient pyramids and other monumental ancient works of art, his lively discussion of other places where we are surprised to find phi is enlightening and entertaining. Whether you are curious to know more about the golden number, the golden ratio, the golden triangle, rectangle, rhombo ...more
May 15, 2008 rated it it was amazing
Recommends it for: geeks, wonderers, adventurers, naturalists, stoners, people with patience
Recommended to Teodora by: ahhhh, math and I go some time back
Between 1 and 2, these pretty whole numbers, lies a number so fascinating that you might be overwhelmed with the beauty of quantifying beauty's perception.
Enter Phi= 1.6180339887....
This humber can explain the difference between the architecture of the Guggenheim as opposed to that of any classical courthouse (picture columns and squares).
The latter are commensurable numbers unlike Phi, which defines rose petal growth, mollusk shell growth, The proportions in Kate Moss's face, and many other be
Jimmy Ele
Jul 17, 2016 rated it it was amazing
I thoroughly enjoyed this book. The appendixes in the back in particular were especially helpful when it came to the Mathematical proofs. The origin of Phi all the way through Fibonacci and beyond was well documented and eye opening. I would recommend this book for anyone who has an interest in Mathematics and/or the history of ideas.
Feb 23, 2012 rated it it was amazing
My never ending quest to comprehend any numbers not addressed in remedial math. This helped a lot. Not dumbed down while not being for physicists only. Very accessible to Land of Oz Pumpkinhead sidekicks like myself.
Jul 06, 2007 rated it it was amazing
Shelves: math
For the love of Fibonacci numbers, roses, geometry and fractals. What do pineapples and spiral galaxies have in common? PHI! This is nerd candy.
Mar 13, 2021 rated it it was amazing
we imagine ourselves walking in a long hallway - a hallway so long that we cannot see the end of it, neither where we came from, and behind us, we hear the sound of a ball which bounces. When we turn around, there is no doubt, there is a bouncing ball. it gets closer and closer. At one point, inevitably, it overtakes us and continues its course, still leaping. And it moves away, until it gradually disappears from our sight. The question is not: is the ball bounces ? Because it is a fact; it boun ...more
Feb 19, 2017 rated it liked it
Shelves: non-fiction
I’m a nerd who loves math. I’m also OCD and have a fixation on numbers. So I’m probably the target audience for a book like this. The book discusses the uniqueness of the golden ratio (represented by the Greek letter phi) and how it has fascinated and interested mathematicians, scientists, and artists throughout history. Livio explains how the number is derived, what it represents, and its unique qualities. As much as I already knew about math, even I learned some cool properties about phi. Did ...more
Jan 27, 2019 rated it really liked it
Shelves: non-fiction
If you have any interest in mathematics--even if you don't have a knack for actually studying it--you should give this book a read. Between the history of the golden ratio, its connections to nature, art, and music, and some philosophical questions about math as a construct, you also get a ton of really fascinating facts about phi, the fibonacci sequence, and other mathematical concepts, some of which were kind of mind-blowing (and can make for great nerdy conversations at dinner parties). ...more
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People read this stuff? 7 83 Aug 07, 2013 06:35AM  

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“Our mathematics is the symbolic counterpart of the universe we perceive, and its power has been continuously enhanced by human exploration.” 6 likes
“Pythagoras was born around 570 B.C. in the island of Samos in the Aegean Sea (off Asia Minor), and he emigrated sometime between 530 and 510 to Croton in the Dorian colony in southern Italy (then known as Magna Graecia). Pythagoras apparently left Samos to escape the stifling tyranny of Polycrates (died ca. 522 B.C.), who established Samian naval supremacy in the Aegean Sea. Perhaps following the advice of his presumed teacher, the mathematician Thales of Miletus, Pythagoras probably lived for some time (as long as twenty-two years, according to some accounts) in Egypt, where he would have learned mathematics, philosophy, and religious themes from the Egyptian priests. After Egypt was overwhelmed by Persian armies, Pythagoras may have been taken to Babylon, together with members of the Egyptian priesthood. There he would have encountered the Mesopotamian mathematical lore. Nevertheless, the Egyptian and Babylonian mathematics would prove insufficient for Pythagoras' inquisitive mind. To both of these peoples, mathematics provided practical tools in the form of "recipes" designed for specific calculations. Pythagoras, on the other hand, was one of the first to grasp numbers as abstract entities that exist in their own right.” 3 likes
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