The Golden Ratio
The Story of Phi, the World's Most Astonishing Number
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Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.From the Hardcover edition.
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Here I go all math geeky again. I picked up this slim book (about 250 pages) a couple years ago and then I started thinking about it and felt compelled to read it. (Voices in my head. You know.) The golden ratio, or phi (pronounced “fee”), was first discovered by Euclid (remember him from geometry class?). Somewhere around 300 B.C. Euclid–
YOU: Whoa-whoa-whoa, wait a minute, Woodge... you actually read another book about math. For fun?! Are you for real?
WOODGE: Yeah, you TV Guide-reading eejit! Get yer head out of your ass! This stuff is interesting!
YOU: You are frikkin high.
WOODGE: Okay, yeah, fine, go back to your latest episode of THE APPRENTICE but I'm talking here so Shut It.
Anyway, Euclid put it thusly: A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser. The resulting ratio is phi, an irrational number equaling approximately 1.6180339887... it goes on forever without repeating a pattern. Phi is said to be the most irrational of irrational numbers. (The most famous irrational number is pi, the ratio of a circle's circumference to it's diameter.) Irrational numbers are called that because they can't be expressed as a ratio of any two rational numbers.
YOU: Dude, I'm falling asleep here.
WOODGE: Oh, don't be such a baby, the book is much more interesting than the nitty gritty of numbers ‘n' stuff.
YOU: Huh? Did you say something? Donald Trump was saying something profound.
WOODGE: Mm-hm.
Anyway, this book was a breeze to read, even I was surprised. It delves into history, art, astronomy, philosophy, poetry, and is full of good quotes and fun historical facts. It also debunks a number of myths associated with the Golden Ratio. Much of this erroneous stuff can be found in other books treated as facts but Mario Livio, a theoretical astrophysicist by trade, gets behind the mumbo jumbo and gives you the straight dope. Maybe you've heard that the Golden Ratio is all over the Parthenon or was a big factor in building the pyramids or was the basis for many of Piet Mondrian's paintings? But that's just wrongedy-wrong-wrong! But some of the diverse places that the Golden Ratio actually does appear includes: the petal arrangements of roses, pentagrams, Platonic solids, the shape of distant galaxies, nautilus shells, and accounting fraud.
Much more than just blathering on about a freakin' number, this book gets into history and touches on Euclid, Pythagoras, Alexander the Great, Galileo, Johannes Kepler (and the fact that his mom was arrested for being a witch – Burn her! Burn her! She's a witch!) and art history, and whether or not God was a mathematician.
And of course there's Fibonacci and his series of numbers which have a very close relationship to phi. The Fibonacci series begins 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89... and each successive number is the sum of the preceding two numbers. If you take one of the numbers and divide it by it's previous number you get closer and closer to phi as you go further in the series. Fibonacci numbers are found everywhere; from the number of petals in a flower, to the number of spirals on a pineapple; to phyllotaxis (Greek for “leaf arrangement”); to the family tree structure of bees, et cetera.
I thought it all was pretty cool to tell you the truth.
WOODGE: So doesn't that sound pretty cool?
WOODGE: Hello? Anybody?
