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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 ...morePaperback, 294 pages

Published
September 23rd 2003
by Broadway Books
(first published 2002)

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## Community Reviews

(showing 1-30)

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

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

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

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

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

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

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 laproporción aureay la secuencia de Fibonacci.

Tras un largo recorrido, finalmente nos descubre que no es posible demostrarni 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 es b ...more

May 15, 2008
Teodora
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 ...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

Sep 24, 2016
Donna Hall
rated it
really liked it
·
review of another edition

Shelves:
snhu,
math-books

Ok, so let me be honest...I am not at all a math fan. In fact, I have a strong phobia of all things mathematical. However, having recently went back to college, I am having to write a sizable paper about Fibonacci and The Golden Ratio. So far, this book has helped me the most. It is easy to read, in mostly plain, understandable language and I might have even enjoyed some parts of it. =)

**"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

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

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“Computer scientist and author Douglas R. Hofstadter phrased this succinctly in his fantastic book Godel, Escher, Bach: An Eternal Golden Braid: "Provability is a weaker notion than truth." In this sense, there will never be a formal method of determining for every mathematical proposition whether it is absolutely true, any more than there is a way to determine whether a theory in physics is absolutely true. Oxford's mathematical physicist Roger Penrose is among those who believe that Godel's theorems argue powerfully for the very existence of a Platonic mathematical world.”
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“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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