11
“Let all who prate of Beauty hold their peace;
Euclid alone has looked on beauty bare.”
– Edna St. Vincent Millay
Issue 11
June 11, 2015
Imagine a room full of preschoolers. Give them each a flute, say, and tell them to go ahead, make noise. And they do. There is no score. Random noises. A cacophony of flute sounds. You listen because you must. Then it dawns on you that you are hearing one chord over and over again. You listen carefully. Not only is that one chord repeated, it is a particularly beautiful chord, repeated at regular intervals. There is something strange going on here. Order within disorder. Beauty within chaos. Mystery.
About 300 years before the birth of Jesus, the Greek philosopher Euclid perceived something similar in the real world, not imaginary but true. In mathematics it shows up as a ratio, 1:1.618. It is called the golden ratio or golden number, and is represented by the Greek letter, Phi, Φ. Consider the below lines. The ratio of AB to AC is 1:1.618 as is the ratio of BC to AB. Compare them and you have a golden proportion. If you make a rectangle of AC and AB or AB and BC, you make a golden rectangle. And on and on to golden triangles, golden pentagrams, golden spirals, pyramids, etc., all echoing 1:1.618. And all, in some strange way, pleasing to the human mind.
A__________________________________C
A_____________________B____________C
Then there is something called the Fibonacci sequence of numbers: 1 1 2 3 5 8 13 21 34 55 and on and on, each number being the sum of the two preceding numbers. The ratio of each number to its neighbor tending toward—1:1.618, the golden ratio!
This golden number shows up in mathematics, architecture, painting, music, the shell of the nautilus, bee hives, flower petals, seeds in an apple, sunflower seeds, leaves on a flower stem, DNA, and on and on. Doubtless more instances will be discovered. (The Golden Rule and the golden mean are important, but they are not part of this golden neighborhood.)
If you want some fascinating fun, look up the golden section or golden ratio. Though you may not look through the eyes of Euclid or Millay, you will be overwhelmed by this golden community, and you might wonder whether it is not a whisper, a hint, of a grand golden world of order and beauty within and beyond everything we can think about.
