Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"Symbol of Perfect Proportion": Review of The Golden Ratio: The Story of Phi, the World's Most Astonishing Number by Mario Livio. Reviewed by Eli Maor. Science, 14 February 2003, page 1016.

A point on the interior of a line segment can be said to divide the segment in two. There is a point on the original segment such that the ratio of the length of the original segment to the length of the larger of the two subdivisions equals the ratio of the length of the larger subdivision to that of the smaller subdivision. This ratio is called the golden ratio. The golden ratio occurs in geometry (as above and as the ratio of the length of a regular pentagon's diagonal to the length of a side), algebra (a solution to x2 - x - 1 = 0), and in nature (because of its connection with the Fibonacci sequence), but it is also claimed to occur frequently in art and in structures such as the Great Pyramid of Egypt. Livio describes several instances of the golden ratio as well as debunking some exaggerated claims of its occurrence. Maor writes that the book "is a timely and welcome addition to the growing body of popular literature on the history of mathematics."

--- Mike Breen