The Golden Ratio by Mario Livio: If you divide a line so that the ratio of the smaller to the larger is equal to the ratio of the larger to the whole, you have the golden ratio, phi. There has been an abundance of literature on the presence of phi in a number of unexpected locations, and this book addresses many of these appearances intelligently. It is organized more or less historically, starting with the Pythagoreans’ obsession with phi (due to its presence in the pentagon and other neat little number tricks) and continuing through the present. The author avoids doctoring numbers to fit phi into famous works of art and architecture, and indeed debunks several such cases. While some of the direct appearances of phi are pretty nifty (such as leaf growth patterns on plant stems), much of the book covers subjects that are only related to phi by a few generations, usually through the pentagon or the Fibonacci numbers. I do not fault the author for this; tangents are to be expected in books about such a narrow subject as a single number.

The final chapter, “Is God a Mathematician,” includes leading theories in response to that question (yes, no, and sort of) and Livio’s personal opinion. I understand the desire to address such a topic, since mathematics is pretty amazing and phi is no small example of this, but this chapter seemed sort of forced, like the author was at a loss on how to wrap up the book. The explanation of the dual nature of light was sort of random, and the rather unsubtle promotion of Stephen Wolfram’s then-unpublished book (which was not well received by the math community) was sort of irritating. I imagine that Livio’s desire was to instill a lingering thirst for knowledge in his reader, to encourage further study, but it felt more like an advertisement for a newfangled religion that will change the way you look at the world. Despite the final few pages, I found this book to be informative and quite readable, which is always high praise for a book about math. Perhaps if Livio had left out his personal opinion I would have finished it feeling more satisfied.

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