X^2 - X - 1 = 0
Journal Entry: Sun Mar 16, 2008, 11:03 AM
- Listening to: Hyenas
- Reading: the bones of a gnu
- Watching: yellow eyes in the darkness
- Playing: for keeps
- Eating: the earth of our ancestors
- Drinking: from the very bottom
X^2 - X - 1 = 0
and
X^2 + X - 1 = 0
Solve and discuss.
Ok, dont solve. These are the equations that produce the golden ratio. The solutions (numerically) are X = .618034 and - 1.618034 and X = - .618034 and 1.618034. Like Pi, e, or any other irrational number both numbers trail into the distance without ever repeating. We call the first X by the Greek letter Phi, and using the exact solution, φ = ½ + sqrt(5)/2. This what we mean when we say the golden ratio.
These numbers interest the fuck out of math geeks like me for a number of reasons, most not worth going into here. But one reason is that the two numbers are inverses, .618034. . . x 1.618034. . . together you get 1.
But both sets of these numbers are difficult to use, and who wants to memorize a quadratic equation. I dont, I just know how to come up with it.
Good thing artist dont need to know them, theres a better way.
Involving rabbits. Immortal rabbits.
Leonardo de Pisa came up with this idea.
First month, Starting with two new born rabbits
New born rabbit start breeding in the second month
Each pair of rabbits produces two more every month
So counting the pairs of rabbits produced you get:
1, 1, 2, 3, 5, 8, 13, 21. . . Each new number is the sum of the previous two, i.e. 5 + 8 = 13. This is called the Fibonacci (Leos nom de math) Sequence. And it shows up EVERYWHERE in living things
The ratio between successive numbers, 2/3, 3/5, 5/8, et cetera, continually approaches the golden ratio, each one closer than the one before. In fact most of the manmade example of the golden ratio uses one of these approximations (Parthenon, Pyramids. . . ).
And these numbers are easy to use.
So try them,
Go golden