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. (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.
The harmonious qualities of the golden ratio-phi-are pleasingly scanned in this history of the number, and, by extension, a historical tour of numbers in general. Phi-1.6180339887...-is never-ending, never-repeating, irrational, incommensurable, one of those special numbers like pi that confound and delight in the same breath. It has been called the divine proportion for its visual effectiveness and Livio, head of the Science Division/Hubble Space Telescope Institute, is willing to concur with this view, although he is also willing to accept that beauty is in the eye of the beholder and the golden ratio (or golden number, golden section, golden this, golden that) may not be primary in its aesthetic appeal. What he is more concerned with here is the frequency of its occurrence in nature, from the petal arrangements on flowers and leaves on stems (phyllotaxis) to the spiral shells of mollusks ("nature loves logarithmic spirals," from unicellular foraminifers to the arms of galaxies) to the apple's pentagram, which simply knows no end to its mysterious implications (mystery and surprise are, Livio notes, much of the joy of mathematics). He traces the history of the number, starting with the mists, proceeding through Euclid, the founder of geometry (it threw the Pythagoreans, who liked tidy numbers, into a fit), Francesca, Leonardo, Dürer, Kepler, to Le Corbusier and contemporary mathematicians. He tackles the grander instances where enthusiasts of phi say the number can be found: the pyramids, the Mona Lisa, the Parthenon. What he finds is that, through juggling the numbers, in almost any work of human creation can be found a golden ratio. The nature of the number itself-and others like theFibonacci series, in which the ratio of successive numbers converges on the golden ratio-beguiles Livio, a keystone to the very meaning of mathematics, concluding that it was both discovered and invented, "a symbolic counterpart of the universe we perceive." Those with math anxiety beware: this portrait of a number would be adrift without its healthy, if accessible, dose of algebra and geometry. A shining example of the aesthetics of mathematics. (Illustrations)