This post has abstract charts because this beautiful sequence is expressed in nature in so many forms that Pantheism has taken the spiral as its symbol. Conscious human recognition and employment of this sequence first occurred in India 2,200 years ago in, surprisingly enough, Pingala’s treatise on Sanskrit prosody. In 1202, Leonardo Pisano Bigollo (known to us as Fibonacci) introduced this description of the spiral to Western scholars through his book Liber Abaci, which generally popularized Indian (via the Arabs) numbers as a useful replacement for Roman numerals.
“Fibonacci Numbers” calculate the growth of phenomena as diverse as buds on a stem to hurricanes and the Whirlpool Galaxy. Generation of it is as simple as starting with zero or one, and then arriving at each subsequent number by adding the previous two.
Here are the first 50 numbers in the sequence:
Put into action, we take squares (or tiles) built upon each other by the same rule and then draw a line bending opposite corner to corner:
In a transient and humble way, I was reminded of the eternal ideal form of this sequence when kayaking from Manhattan’s west side to Sandy Hook, NJ. Each paddle stroke created a little vortex, a spiral, as is demonstrated by this photo by Björn Olin I grabbed off the Web.
By pondering the mathematics behind the swirls, I felt the presence of our predecessors who revealed the sequence. I was no longer alone. Drawing upon another poetic tradition, I wrote this Haiku:
Paddle dip and stroke.
Pier 40 to Sandy Hook