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# The Golden Ratio: The Story of PHI, the World's Most Astonishing Number

by
Mario Livio (Goodreads Author)

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 ...moreKindle Edition

Published
(first published 2002)

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## Community Reviews

(showing 1-30)

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

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

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

Mar 15, 2011
Woodge
rated it
really liked it
·
review of another edition

Shelves:
non-fiction,
mathematics

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

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

**a/b=(a+b)/a=phi**.

In mathematics, there are many ways to express t ...more

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

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

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

I'll admit it's not very catchy, but it ...more

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

May 11, 2009
Cassandra Kay Silva
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.

This book is a mathematical utopia.

A must read.

*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

When Livio does manage to address phi directly, he does so by debu ...more

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

May 15, 2008
Teodora
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

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

Jul 17, 2016
Jimmy Ele
rated it
it was amazing
·
review of another edition

Shelves:
uber-favorites,
foundation

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.

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.

**"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

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

Dec 17, 2016
Gabrielam13
rated it
really liked it
·
review of another edition

Shelves:
popularizarea-stiintei,
matematica

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

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People read this stuff? | 7 | 81 | Aug 07, 2013 06:35AM |

1 trivia question

More quizzes & trivia...
“Our mathematics is the symbolic counterpart of the universe we perceive, and its power has been continuously enhanced by human exploration.”
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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.”
—
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