September 1, 2014

Review: The Glorious Golden Ratio by Alfred S. Posamentier & Ingmar Lehmann..

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At the heart of all science is the mathematics that makes it “tick”. And while math drives the universe, some of the curious relationships that arise are, well, just down-right bizzaro. Such is the topic of this week’s review entitled The Glorious Golden Ratio by Alfred S Posamentier & Ingmar Lehmann and published by Prometheus Books. The golden ratio has been known since antiquity and pops up in some unsuspecting places. Signified by the symbol “ɸ” The golden ratio is simply the division point at which the larger section has the same ratio to the whole as the second smaller section has to the larger. (Phew, a simple home-brewed explanation sans wiki, people!) This comes down to an approximation of 1.61803398874989484820458683436563…. ad infinitum, much like another famous non-repeating decimal, pi. Curiously, the reciprocal of ɸ (1/ɸ, remember your high school math, people!)  is 0.61803…. or ɸ – 1, the only number for which this is true! But it gets stranger from there; the authors of The Glorious Golden Ratio do not back away from the “Mathiness,” in a way that would make Buffy’s Giles proud. Kepler himself compared the Pythagorean Theorem to “a heap of gold” while the golden ratio to “a precious jewel”. If God is indeed a geometer, he must have an affinity for this ratio that pops up in the strangest of places. Of course, Kepler spent much of his academic life chasing a supposed link between the five perfect solids and the then known five planets, a caveat against reading too much into mathematical coincidences.

Still, the authors do a good job with relating the golden ratio and its various instances across geometry, architecture, and even in nature, as well as its close relationship with the Fibonacci sequence. Did you know that the golden ratio pops up in fractal patterns? Or in the “Cross of Lorraine”? Or in the leaves of a daffodil? Or in Illinois (!) I don’t pretend to understand all of the “mathiness” contained within the covers of this book, although our 43-year old brain can still hold its own. And yes, it sent me off measuring the golden ratio noted by Leonardo da Vinci between the height of my navel versus overall height! (Hey, something had to fall around 0.61803…)

But such is the Sunday afternoon fun that one can have with mathematics. Wisely, the authors do not draw any mystical/metaphysical connections with these curiosities, but instead use them as a teachable moment to demonstrate how math pops up, all around us. And of course, it’s fascinating to conjecture as to just when ancient man became aware of the golden ratio. And on the astro-biological tip, we wonder if E.T. might be beaming the golden ratio and/or it’s reciprocal at us, instead of pi or prime numbers? Has Jodi Foster or Seth Shostak checked into this?

Do check out The Glorious Golden Ratio as a serious straight up low-down sans Woo of all that is ɸ… and don’t forget to celebrate “Golden Ratio Day” next January 6th at 18:03! (Hey, its never too early to hype!)



  1. [...] on such mathematical odysseys as Pi: A Biography of the World’s Most Mysterious Number & The Glorious Golden Ratio, also recently reviewed on this [...]

  2. [...] site and Posamentier & Lehmann’s work will also recall our reviews of their fascinating works, The Glorious Golden Ratio & The Secrets of Triangles a while [...]

  3. [...] of this space will also remember our reviews of The Glorious Golden Ratio, The Secrets of Triangles and Magnificent Mistakes also by Lehmann and [...]

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