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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

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3.76  ·  Rating details ·  4,813 Ratings  ·  290 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
Kindle Edition
Published (first published 2002)
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Brad
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.

Howev
...more
Sabio
Jul 11, 2007 rated it liked it  ·  review of another edition
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
...more
Jasmine
Jul 10, 2011 rated it it was ok  ·  review of another edition
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
...more
Woodge
Mar 15, 2011 rated it really liked it  ·  review of another edition
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!
...more
Jill
Aug 03, 2014 rated it really liked it  ·  review of another edition
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
Ms.pegasus
Dec 02, 2014 rated it really liked it  ·  review of another edition
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
...more
Tim
Apr 01, 2009 rated it really liked it  ·  review of another edition
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 th ...more
Ob-jonny
May 05, 2014 rated it really liked it  ·  review of another edition
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
EJ Natale
May 20, 2011 rated it did not like it  ·  review of another edition
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
...more
Mikael Lind
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
...more
Gendou
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.
...more
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
...more
Rosemary Paul
Jan 11, 2013 rated it it was amazing  ·  review of another edition
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
...more
Cassandra Kay Silva
May 11, 2009 rated it it was amazing  ·  review of another edition
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.
White
Aug 26, 2009 rated it it was amazing  ·  review of another edition
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.
Shaw
Dec 19, 2015 rated it it was amazing  ·  review of another edition
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.
David
May 11, 2013 rated it it was amazing  ·  review of another edition
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
...more
Andres-Leonardo

Mario Livio aborda un análisis crítico de las numerosas referencias históricas que han relacionado en algún momento arte con la proporción aurea y la secuencia de Fibonacci.

Tras un largo recorrido, finalmente nos descubre que no es posible demostrar ni una sola obra pictórica, musical, escultórica o arquitectónica que tenga relación documentada con la proporción aurea.

¡Pues que desilusión! Todo parece ser fruto de un insistente trabajo de aficionados a la mistica de todos tiempos.

El relato e
...more
Mark
Aug 03, 2011 rated it it was amazing  ·  review of another edition
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
Teodora
May 15, 2008 rated it it was amazing  ·  review of another edition
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
...more
Jimmy Ele
Jul 17, 2016 rated it it was amazing  ·  review of another edition
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.
Chris
Feb 23, 2012 rated it it was amazing  ·  review of another edition
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.
Tung
Feb 19, 2017 rated it liked it  ·  review of another edition
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
Vanessa Torres
Se me hizo un libro difícil de digerir, es un libro acerca de la historia de las matemáticas y su relación con el número phi, así que habla de conceptos, de personas, de demostraciones, de arte y de música a lo largo de la humanidad.

Lo que si es que deja sembrada la curiosidad acerca de lo mágico que tienen las matemáticas, de lo mágico de la proporción áurea y de como las matemáticas están en todo, lo cual no es ninguna novedad.
Eleclyah

"La sezione aurea" ovvero "Opere famose che non hanno nulla a che spartire con ɸ"
Non è mia abitudine lasciare da parte un libro, ma quando è troppo, è troppo.
La storia di ɸ, un numero irrazionale che vale 1,618..., e del suo sorprendente ricorrere negli ambiti più svariati, è un argomento che ben si sarebbe prestato alla stesura di un saggio valido.
Quello di Mario Livio mi ricorda vagamente un trattato esoterico un po' fuori luogo, in cui gli appassionati di ɸ (categoria di cui lui, per fortuna,
...more
Peter Lanagan
This was a book I really wanted to like.

Author Marco Livio describes the history of the Golden Ratio (Phi), an irrational number which has been imbued with special meanings by some. Livio explored the history of the philosophy of mathematics starting with the Pythagoreans and follows developments in mathematical philosophy to the present day. The author uses this history to explore how Phi shows up in nature such as with the distributions of leaves on planets, the spiral of a conch shell, and th
...more
Upom
The Golden Ratio turned out to be somewhat interesting, but ultimately tedious book about phi. The book does a decent job of covering what exactly phi is, its fantastic mathematical properties, as well as some of its appearances in nature. That being said, much of the books is a critique of where it DOESN'T appear. Although debunking claims of appearing in the golden pyramids and art is important in scholarship, it certainly takes away from the magic of the number, as well as makes for boring re ...more
Gabrielam13
Mi-a plăcut foarte mult această carte pentru că am învățat foarte multe lucruri pe care nu le știam, cum ar fi legătura dintre șirul lui Fibonacci și Phi, cât și multe alte proprietăți fascinante ale lui Phi. Însă dincolo de noutățile matematice însoțite de explicații foarte simple și ușor de înțeles, mi-a plăcut că Mario Livio a făcut o prezentare exhaustivă a conceptului, prezentându-l nu numai din punct de vedere istoric și analizând evoluția lui în matematică, ci și influența pe care a avut- ...more
Gary
Jul 28, 2014 rated it it was amazing  ·  review of another edition
I really enjoyed this. The scope of the book was great, through history with stops at art, architecture, music, galaxies, and snails. I really appreciated the skeptical debunking of a lot of the golden ratio claims made about the Pyramids, Parthenon, and even the Mona Lisa. With that nonsense out of the way what really blew my mind was the "surprise" aspect of how the golden ratio turns up in the solutions to other problems. And finally, the last chapter was probably my favorite... the philosoph ...more
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People read this stuff? 7 81 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.” 3 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.” 2 likes
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