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 defined 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 the crystals of some materials, to the shapes of galaxies containing billions of stars. 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 suggested that it is connected to the behavior of the stock market!” The Golden Ratio is a 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 one of the greatest treasures of geometry; such medieval thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Debussy, Le Corbusier, 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.

Read a review of The Golden Ratio by Dr. Helen Joyce. Additionally, Dr. Livio has an article on the Golden Ratio and Aesthetics in +Plus Magazine.

The Accelerating Universe

In one of the most surprising and important findings in cosmology in the century, astronomers recently discovered that the unierse may be expanding at an ever-increasing rate. This discovery of an “accelerating universe” stunned many cosmologists because it directly contradicts their most deeply held beliefs about the evolution and fate of the universe. The discovery has therefore ignited a new revolution in cosmology in which scientists are wrestling anew with the most fundamental questions and revisiting ideas that were dismissed long ago.

As leading astrophysicist Mario Livio explains in this elegantly written and timely book, most cosmologists have long believed that the universe will expand at a gradually decreasing rate until the expansion effectively stops. In this pleasing scenario, the universe is perfectly poised between expanding into oblivion or collapsing in a “big crash” and will continue on in this miraculously balanced state for eternity. The discovery that the expansion appears in fact to be speeding up - and therefore that the universe will keep expanding faster and faster for infinity - throws the view of a perfectly balanced “beautiful universe” into question. Even more troubling, it threatens the cherished belief that the fundamental laws governing the cosmos are in themselves exquisitely “beautiful,” a belief that has always been a guiding light of discovery in cosmology.

What can explain this accelerated expansion? Does the universe have much less mass than originally thought? Is there some exotic unknown force, or new kind of energy, causing acceleration? Was Einstein’s “greatest blunder” - his idea of a cosmological constant - the right idea after all? What will the ultimate fate of the universe be? Must there be beauty in all good theories of the cosmos? Or are some of the laws governing the universe “ugly”?

In an entertaining and lively exploration of the answers to all of these questions, Mario Livio introduces readers to the “old cosmology,” which culminated in the view of the perfectly balanced universe, and then presents all of the ideas being explored by cosmologists in the “new cosmology” as they come to terms with the discovery of acceleration. Offering extraordinarily clear explanations of all the key concepts and theoretical ideas, Livio is a marvelous guide through this most exciting frontier in science today.