





Winner, 2004 Outstanding Academic Title, Choice Magazine
"An enlightening, fascinating, wellillustrated, literate and (usefully) opinionated discussion. Covers historical, mathematical, and realworld appearances of the famous number. Of special interest are debunkings of some hoary myths (e.g., about the Parthenon) and connections to crystals, fractals, and music." —The American Mathematical Monthly
Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In The Golden Ratio, Mario Livio explores the 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 also been suggested that it is a good predictor of 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 phifixated 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.
Ideal reading for students in Introductory Physics, Mathematics, and Interdisciplinary courses.
"Mario Livio's The Golden Ratio provides a wonderful springboard to the amazing world of mathematics and its relationship to the physical world, as viewed from ancient to modern times." —Roger Penrose, Rouse Ball Professor of Mathematics, Oxford University, author of The Emperor's New Mind
"Theoretical astrophysicist Livio gives pi's overlooked cousin phi its due with this lively account....Livio is gifted with an accessible, entertaining style....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."—Publishers Weekly
“A shining example of the aesthetics of mathematics.”—Kirkus Reviews
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.

