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The Golden Ratio: The Story of PHI, the World's Most Astonishing Number, by Mario Livio
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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.
- Sales Rank: #40593 in Books
- Brand: Broadway Books
- Published on: 2003-09-23
- Released on: 2003-09-23
- Original language: English
- Number of items: 1
- Dimensions: 8.01" h x .67" w x 5.18" l, .51 pounds
- Binding: Paperback
- 294 pages
- Broadway Books
From Publishers Weekly
Most readers will have at least dim memories from geometry class of the irrational number pi. Theoretical astrophysicist Livio gives pi's overlooked cousin phi its due with this lively account, the first on the subject written for the layperson. Phi is the golden ratio of antiquity (1.6180339887), a never-ending number so lauded for its harmonious qualities that in the 16th century it was dubbed the divine proportion. It is related to phenomena as diverse as the petal arrangements of roses, the breeding patterns of rabbits and the shape of our galaxy. Phi is also claimed to have been crucial in the design of the Great Pyramids, the composition of the Mona Lisa and the construction of Stradivarius violins. Livio (The Accelerating Universe) carefully investigates these and other claims and does not hesitate to debunk myths perpetuated by overzealous enthusiasts he calls "Golden Numberists." This is an engaging history of mathematics as well, addressing such perennial questions as the geometric basis of aesthetic pleasure and the nature of mathematical objects. Useful diagrams and handsome illustrations of works under discussion are amply provided. Livio is gifted with an accessible, entertaining style: one typical chapter bounds within five pages from an extended discourse on prime numbers to a clever Oscar Wilde quote about beauty to an amusing anecdote about Samuel Beckett and finally to an eminently clear explanation of G"del's incompleteness theorem. With a guide to the history of ideas as impassioned as Livio, even the math-phobic can experience the shock and pleasure of scientific discovery. This thoroughly enjoyable work vividly demonstrates to the general reader that, as Galileo put it, the universe is, indeed, written in the language of mathematics.
Copyright 2002 Reed Business Information, Inc.
From School Library Journal
Adult/High School-Take something as simple as a line segment and mark it at just the right place. Looking at it with a mathematician's eye, an interesting relationship appears: the ratio between the whole line and the larger of the pieces it was broken into is the same as the ratio of the larger piece and smaller piece. Better known as "the golden ratio" or phi, 1.618- is a number that has fascinated humans for several hundred years, and people have claimed evidence of phi in all manner of things. Livio takes readers on a treasure hunt for phi from ancient times through the present. On the way, he debunks a number of popular myths (e.g., the notion that Mondrian used it in his abstract paintings) and does a wonderful job explaining the Fibonacci sequence and its relationship to phi. Small, black-and-white photos and reproductions demonstrate items mentioned in the text. While it may seem that the author wanders in his expositions, his excursions into history and number games add fun and depth for those who wish to follow. To get the most out of The Golden Ratio, it is best to have an understanding of algebra and basic trigonometry, although the book is great for general readers who don't mind working a little to gain a lot of understanding.
Sheila Shoup, Fairfax County Public Library, VA
Copyright 2003 Reed Business Information, Inc.
From Scientific American
Most schoolchildren learn the importance of the number ϖ, or pi (3.14159...), early on in their mathematical training. The area of a circle? ϖ (r2). Circumference? 2ϖr. But for astrophysicist Livio, the number φ, or phi (1.61803...), holds more wonder. Known as the Golden Ratio, Golden Number and other names related to gold or divinity, phi can be used to describe the characteristics of seashells, sunflowers, paintings and pentagrams. Livio traces the history of phi's discovery in tandem with the development of arithmetic, algebra and higher mathematics, examining along the way whether its value was factored into the construction of the Egyptian pyramids or the Parthenon of Greece. Practical examples placed throughout the story, requiring nothing more than a handheld calculator or some scratch paper, help to illustrate phi's relevance to mathematics and the world at large.
Editors of Scientific American
Most helpful customer reviews
3 of 3 people found the following review helpful.
Mario Livio takes us on such an engaging and intelligent journey on the history of number and mathematics
By rustberg
Dr. Mario Livio takes us on such an engaging and intelligent journey on the history of number and mathematics. The carrot is the search for the golden ratio, and he certainly delivers on that in unexpected ways, debunking common misconceptions such as golden ration being the basis for the pyramids, the parthenon, and many famous artworks. On the other hand, he shows that the actual properties of the golden ratio continue to reveal even greater secrets! The deeper theme of the book is the relationship between mathematics and the real world—does mathematics reflect our universe or does our universe strive to conform to mathematics (a Platonic view)? The excitement and enthusiasm for this pursuit sparkles throughout the book.
4 of 4 people found the following review helpful.
Interesting, but would recommend more for entertainment than education
By SharpieAndDuctTape
I'm an engineer/applied math that was assigned to read this book for a elective college course. The class concluded that the book was a fun and an interesting read, but it accomplished that through seemingly dramatized and exaggerated arguments/points. The arguments presented were more on the side of "interesting thought candy" than something to be taken seriously academically. Overall a good read, and will do so again, but reading it the fist time immediately turns you into a skeptic, maybe that's the point?
4 of 4 people found the following review helpful.
The World's Most Astonishing Number (most of the time)
By Kiel Basford
Mario Livio gives an accessible and objective history of the occurrences and uses of the Golden Ration. He makes a strong argument for Phi as "the world's most astonishing number" while at the same time mitigating some of the more radical claims about the number and its influence through history.
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.
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