In “The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number,” Livio traces the discovery of phi back to ancient Greeks who noticed that when a line is divided into two unequal sections, the ratio of the longer part to the shorter is in the “golden proportion” if it equals the ratio of the whole line to the longer section. First dubbed the “divine proportion” by a 15th-century friar who argued that it was the most esthetically pleasing ratio, by the 20th century the number–now called phi–had developed a cult following among scientists and amateurs for its reported appearance in nature and art. Livio writes that spirals based on the ratio can be seen in microscopic protozoa, mollusks and galaxies of stars, as well as the arrangements of petals in a rose or seeds in a sunflower. The architect Le Corbusier deliberately used it in his designs, as did artists like Salvador Dali and German Renaissance painter Albrecht Durer.
Are such appearances real or imained? “In nature, there is no question that it is really there in many places,” says Livio. Yet phi’s prevalence in works of art stems not from artists’ unconscious appreciation of its beauty but from their “awareness of the legacy of this number and all its history.” Livio places that history solidly in the cultural context of each age, peppering this eloquent book with quotes from Shakespeare and Keats as well as Galileo and Einstein. In the process, he succeeds in the unlikely task of bringing a number to life.
