The Golden Ratio: The Story of PHI, the World’s Most Astonishing Number

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.From the Hardcover edition.


The Golden Ratio is a book about one number—a very special number. You will encounter this number, 1.61803 , in lectures on art history, and it appears in lists of “favorite numbers” compiled by mathematicians. Equally striking is the fact that this number has been the subject of numerous experiments in psychology.

I became interested in the number known as the Golden Ratio fifteen years ago, as I was preparing a lecture on aesthetics in physics (yes, this is not an oxymoron), and I haven’t been able to get it out of my head since then.

Many more colleagues, friends, and students than I would be able to mention, from a multitude of disciplines, have contributed directly and indirectly to this book. Here I would like to extend special thanks to Ives-Alain Bois, Mitch Feigenbaum, Hillel Gauchman, Ted Hill, Ron Lifschitz, Roger Penrose, Johanna Postma, Paul Steinhardt, Pat Thiel, Anne van der Helm, Divakar Viswanath, and Stephen Wolfram for invaluable information and extremely helpful discussions.

I am grateful to my colleagues Daniela Calzetti, Stefano Casertano, and Massimo Stiavelli for their help with translations from Latin and Italian; to Claus Leitherer and Hermine Landt for help with translations from German; and to Patrick Godon for his help with translations from French. Sarah Stevens-Rayburn, Elizabeth Fraser, and Nancy Hanks
provided me with valuable bibliographical and linguistic support. I am particularly grateful to Sharon Toolan for her assistance with the preparation of the manuscript.

My sincere gratitude goes to my agent, Susan Rabiner, for her relentless encouragement before and during the writing of this book.

I am deeply indebted to my editor at Doubleday Broadway, Gerald Howard, for his careful reading of the manuscript and his insightful comments. I am also grateful to Rebecca Holland, Publishing Manager at Doubleday Broadway, for her unflagging assistance during the production of this book.

Finally, it is due only to the continuous inspiration and patient support
provided by Sofie Livio that this book got written at all.

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