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The Golden Ratio
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The first book for the layperson on a mathematical relationship that has obsessed mathematicians, philosophers, scientists, and artists since ancient Greece--an omnipresent number considered to be "divine."
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About the Author

Mario Livio is head of the Science Division at the Hubble Space Telescope Institute, where he studies a broad range of subjects in astrophysics, particularly the rate of expansion of the universe. He is the author of one previous book, The Accelerating Universe (2000). He is a frequent public lecturer at such venues as the Smithsonian Institution and the Hayden Planetarium. He lives in Baltimore, Maryland. From the Hardcover edition.

Reviews

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 Gedel'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. (Oct. 29) Copyright 2002 Cahners Business Information.

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.

"[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

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