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The Golden Ratio, by Mario Livio
The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number, by Mario Livio, Broadway Books, 2002.
Imagine a line from A to C, with point B somewhere in between. If AC/CB=AB/AC, then both these ratios will be the golden ratio phi, 1.6180339887…, (1+sqrt(5))/2. You might not think that an entire book could be written about this, but Dr. Livio, head of the Science Division at the Space Telescope Science Institute, did.
This number turns up in logarithmic spirals, platonic solids, Penrose tessellations, and is deeply connected to Fibonacci numbers. Oddly, phi is 1.618…, phi^2 is 2.618…, and 1/phi is 0.618… This book is filled with this sort of amazing trivia.
A good part of The Golden Ratio consists of debunking claims that phi was used in the pyramids and other ancient structures and in more recent paintings and other art. Make enough measurements (with big enough error bars) and you can find any number anywhere. The only way to be sure is if the artist said so, and there are a few such examples.
I did feel that it started off a bit dull and got more steadily more interesting as I read it. That may be a quirk of my personal interests. You may wish to skip around a bit if part of it is not of great interest to you. It is probably not a very useful book, but some people (you know who you are) will find it fascinating. I did.
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