Why I read it: An unnerving love of numbers.
Summary: The irrational number Phi (pronounced "fee") has baffled mathematicians for centuries, much like Pi. The author defines it and seeks its historical applications. He works hard to debunk theories of its usage in ancient times in the construction of the pyramids, in Greek architecture, etc. He also discusses its theological ties through time, as science played with the border between cold hard facts and the unknown and supernatural.
My Thoughts: Ha! Where do I begin? I guess with nature, as I'm a naturalist by profession (these days). The concept of the logarithmic spiral is the key to linking the number to nature. To define Phi in basic terms, if you have a straight line cut into two parts, and the ratio of the sum of the quantities of the two parts is equal to the ratio of the larger to the smaller, you have the Golden Ratio:
a + b/a = a/b = Phi
The number attained is approximately 1.6, but like Pi, it goes on forever with no discernible pattern. Hence the determiner "irrational." More on that in a minute.
As for the logarithmic spiral, if you took a Golden Ratio rectangle and drew a line across it at the point where the ratio is defined, you would find that you've created a second, smaller, Golden Ratio rectangle. Do it again with that smaller one, and you've done it again. This process can continue forever, falling into ever smaller rectangles. You've created a spiral that manifests itself in nature repeatedly: in spirally-formed seashells, in the spiral arms of galaxies, even in the way a peregrine falcon dives for its prey. Because of the fact that its eyes are on the side of its head, it cannot dive straightforward. If we were to stand at the top of the falcon's dive and watch it fade farther and farther away, we'd see the Golden Ratio in action.
Here's my contribution to the topic: chimney swifts. If you've ever watched a chimney swift diving for its nest in, yes, a chimney, you've noticed that it does not dive in a straight line either. It has an arc to it, due, again, to the positioning of its eyes on its head, that I'll bet is relative to the Golden Ratio. But the bigger question remains: what were chimney swifts called before chimneys? If they nested in hollowed out dead trees, were they known as snag swifts? Anyway, back to the math.
Livio's book is filled with the history of the number, and the history of speculation about the use of the number in art, architecture, poetry, etc. From this standpoint, it is thoroughly entertaining. He spends a lot of time debunking, as good scientists will do, and I now wonder who's rebutted his debunking. Such is the beauty of the study of any singular topic in history. There's always another opinion.
I read a term in this book I had not encountered before: recreational mathematics. Math for fun. As a high schooler, I hated math, hated it with vigor. Oddly enough, though, when it came time for my SAT's, I scored much higher on my math test than I did my English. Go figure. Well, I did. I looked back at my life. As a toddler, I memorized the serial numbers on the undersides of my Matchbox cars. When baseball cards were discovered, well, I don't even have to go into that. Every player, every stat. My friends and I even developed statistically-based baseball and professional wrestling games that generally fell into the right results: Jim Rice always had more home runs than Spike Owen. Today, I lead our local citizen science efforts, compiling reams of data that I twist and turn every way possible looking for trends, sometimes answers. Ive been a recreational mathematician all my life.
My favorite story in this book, though, had to do with the Pythagoreans. What a wacky bunch. They were so upset when a colleague discovered an irrational number that they built a tomb for him and acted like he was dead. I don't know if the world's professional mathematicians today would react so strongly, but it's amazing to me how passionate they were about math and its consequences. I think, though, that it's a key to life; without that internal fire, is life really worth living?