Book Review: The Golden Ratio, Volume 52, Number 3

The number (1 + √ 5)/2 = 1.618 … is widely known as the golden ratio, φ and phi. Phi appears in many different equations and formulas and has many interesting properties. Many people have heard marvelous tales about phi and how it permeates art and nature. My first exposure to phi was in a comic book entitled Donald in Mathmagic Land, which later became an animated cartoon seen by millions of people. As I grew up I kept seeing the same " facts " repeated in many different places, including popular books on mathematics, various mathematics textbooks, newspapers, and even in scholarly papers. It seemed as if everybody knew these basic " facts " about phi. Around 1990 I decided to give a talk to the University of Maine Classics Club and thought that the golden ratio would be a fascinating topic for this audience. During the preparation of the talk I collected all of the usual stories about the golden ratio being used to design the Great Pyramid and the Parthenon, as well as about its aesthetic properties and its use by painters. I found the references to be quite vague, and in the process of trying to make my talk more precise, I actually began to look up measurements of buildings. Much to my surprise, the results did not support the claims that were being made about the golden ratio. The results of my research were published in " Misconceptions about the Golden Ratio " (The paper debunks many of the more prominent claims about phi and documents their pervasive presence in the mathematical literature. For example, the name " golden ratio " is a nineteenth-century creation and is not an ancient name for phi. Furthermore, it does not appear that phi was used to design either the Great Pyramid or the Parthenon. For example, the Parthenon is 228 feet and 1/8 inch long, 101 feet and 3.75 inches wide, and 45 feet and 1 inch high. Taking the obvious ratios of length/width and width/height yields the number 2.25, which is quite far from phi, which is 1.618…. The number 2.25 = 9/4 is the ratio of two squares, and further study indicated that the gate to the Acropolis was built using this same ratio. It also does not appear that Leonardo da Vinci used phi, nor is phi present in the proportions of the United Nations …