The Golden Ratio.

Some recent ESPN links: Analyses of the Jays/Astros ten-player trade and the Brett Myers trade, as well as a big post on players I’ve scouted in the AZL over the last week, including Jorge Soler. The Conversation under the Myers piece has been rather bizarre, as a few (presumably male) readers are saying I shouldn’t have brought up Myers’ 2006 arrest on domestic violence charges. Needless to say, I think these complaints are spurious.

—

I’m a big fan of mainstream books about mathematics, most of which would probably be best classified as “history of math” even if they’re discussing a currently unsolved problem, such as John Derbyshire’s excellent book on the Riemann Hypothesis, Prime Obsession. (And yes, I’m aware of Derbyshire’s political writing, but that doesn’t change the fact that the Riemann book is very well done.) Mario Livio’s book The Golden Ratio: The Story of φ, the World’s Most Astonishing Number was on my wish list for a long time because it seemed like a perfect blend of the academic and applied branches of mathematics, as the irrational number φ appears in numerous places in nature and (I thought) art. Unfortunately, Livio’s book spends more time talking about where φ is not than about where it is, making this more of a book of mythbusting than of math.

Livio does provide a solid introduction to φ, an irrational number equal to (1 + √5)/2 = 1.6180339887… that has several interesting properties, including:

* φ² is equal to φ + 1, or 2.6180339887…
* 1/φ is equal to φ – 1, or 0.6180339887…
* If you take any line segment AB and place a point C on it such that the ratio of the longer half to the shorter half is equal to the ratio of the entire segment to the longer half, the ratio in question will be equal to φ
* The ratio between consecutive terms in the Fibonacci sequence – the series 0, 1, 1, 2, where each successive term is equal to the sum of the two terms before it, thus continuing with 3, 5, 8, 13, 21, ad infinitum – approaches φ. The ratio between the 17th and 16th terms is already 1.61800328…
* φ is also the result of the peculiar expression

The golden ratio also appears in many polygons and polyhedrons of interest not just to mathematicians but to artists, architects, and even botanists, as it appears in the spacing of leaves around the stems of many plants. But interest in the ratio has spurred no end of specious or outright fictitious claims about its appearance, including an oft-repeated one about its inclusion in the dimensions of the Parthenon (obtained by gaming the measurements to achieve the desired result) and another claiming Leonardo da Vinci used it in the Mona Lisa (similarly bogus). Livio devotes so much of the book to debunking these and other claims that by the time he gets around to discussing the golden ratio’s actual appearances in art, architecture, and nature, he’s devalued his subject by spending too little time explaining where φ is and too much time explaining where it ain’t.

Next up: I’m a bit behind here, having already finished Michael Ruhlman’s superb The Making of a Chef: Mastering Heat at the Culinary Institute of America, the book that first established him as one of the best writers on food and cooking today.