I picked up a book a few years ago called The Golden Ratio: The Story of Phi, The World’s Most Astonishing Number.
I have been reading and re-reading it for the past two years and have never really gotten a good sense of it. I get that it has to do with the Fibonacci Sequence, but I am not a math major. While the idea of Φ (phi) makes sense to me, the nuts and bolts of why it makes sense don’t… make sense. I mean it is the number or ratio I use when I don’t have an image in my head – chamfering an edge on a piece of wood, establishing a ratio of height-width, et-cetera. 1.618 just works.
So I re-read and play around with it, but it just doesn’t set in my brain.
And then I stumbled across this thread the other day on Metafilter. It is about a 13 year old kid who is experimenting with Fibonacci to harness solar power more effectively based on his observations of trees.
Then my friend Erin posts a link to this story. And all of the sudden it makes sense. The article isn’t very well written. It seems rushed and a little cobbled together, but it has this:
My investigation started with trying to understand the spiral pattern. I found the answer with a medieval mathematician and an 18th-century naturalist. In 1209 in Pisa, Leonardo of Pisano, also known as “Fibonacci,” used his skills to answer a math puzzle about how fast rabbits could reproduce in pairs over a period of time. While counting his newborn rabbits, Fibonacci came up with a numerical sequence. Fibonacci used patterns in ancient Sanskrit poetry from India to make a sequence of numbers starting with zero (0) and one (1). Fibonacci added the last two numbers in the series together, and the sum became the next number in the sequence. The number sequence started to look like this: 1, 1, 2, 3, 5, 8, 13, 21, 34… . The number pattern had the formula Fn = Fn-1 + Fn-2 and became the Fibonacci sequence. But it seemed to have mystical powers! When the numbers in the sequence were put in ratios, the value of the ratio was the same as another number, φ, or “phi,” which has a value of 1.618. The number “phi” is nicknamed the “divine number” (Posamentier). Scientists and naturalists have discovered the Fibonacci sequence appearing in many forms in nature, such as the shape of nautilus shells, the seeds of sunflowers, falcon flight patterns and galaxies flying through space. What’s more mysterious is that the “divine” number equals your height divided by the height of your torso, and even weirder, the ratio of female bees to male bees in a typical hive! (Livio)
And there you have it. The sequence explained. I think I am going to pick up the book again once classes start and take another crack at it. I think I can really get it this time around.