- Paperback: 294 pages
- Publisher: Broadway Books; Reprint edition (September 23, 2003)
- Language: English
- ISBN-10: 9780767908160
- ISBN-13: 978-0767908160
- ASIN: 0767908163
- Product Dimensions: 5.2 x 0.7 x 8 inches
- Shipping Weight: 9.6 ounces (View shipping rates and policies)
- Average Customer Review: 167 customer reviews
- Amazon Best Sellers Rank: #50,071 in Books (See Top 100 in Books)
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The Golden Ratio: The Story of PHI, the World's Most Astonishing Number Paperback – September 23, 2003
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“[An] entertaining review of the history of mathematics . . . A nice mental workout.” — Linda Schlossberg, San Francisco Chronicle
“Engagingly enthusiastic . . . It’s hard not to feel inspired and even unsettled by the hidden order Livio reveals.” — New Scientist
“Numbers aficionados will delight in astrophysicist Livio's history of an irrational number whose fame is second only to that of pi. . . . Livio's encyclopedic selection of subjects, supported by dozens of illustrations, will snare anyone with a recreational interest in mathematics.” — Booklist
From the Inside Flap
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 than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!
The Golden Ratio 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 believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.
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If it's been a few years since you finished school and like me you "returned" most of the higher math you learned to the teacher (as they say in Mandarin Chinese), you may have to concentrate to follow some of the math proofs.
On a personal level, I am tempted to use Benford's Law in our local community center to engage a few of the local leaders. I hope I can find time in the next few weeks! Also, this book also leaves me wanting to read Livio's latest book "Is God a Mathematician?" and a few recent works by others on chaos theory and complexity systems.
The intricacies of Phi and the surprising places it turns up will certainly be more appreciated given some knowledge of mathematics, but Livio took care to invite the lay reader. His writing, while sometimes technical, is never intimidating, and the hard stuff is nicely tucked in the book's appendices for reader's with a mathematical background to dissect.
The book has two main points - one to simply elucidate what Phi is, how its value was obtained and where it's found in mathematically related disciplines and natural phenomena. The other is to determine the validity of claims of humanity's use of it through history - for instance, its use in the construction of the Pyramids of Egypt. When Livio deals with this latter point, he is never romantic and always objective. He analyzes arguments that have been made for Phi's presence in art and architecture and comes to an unambiguous conclusion about Phi's aesthetic merit. I found no reason to disagree with any of his arguments, but I did occasionally find them to be overly exhaustive, particularly when it turns out that certain people thought Phi to be a bit more astonishing than is actually the case. Still, Livio is a cogent writer, and his book is probably the best place to start if you'd like to learn about Phi.
This book is not only fun to read (for a non-mathmetician type), it is fairly easy to understand (not a quick read, and at some points it takes some effort), and I would guesstimate about 80% English, 10% essential illustrations, and 10% math.
And, since I find all this dynamic symmetry and Phi stuff fascinating--and do not want to go back to school to learn advanced algebra and trig--this book is a godsend!
One more thing. This is written by a scientist that can write for non-scientists. He has done his research very thoroughly and covers the subject comprehensively.