The Fibonacci Sequence

Of all the mathematical patterns discovered throughout history, none have had the profound impact as the Fibonacci Sequence. Originally discovered in ancient India, the sequence was not formally known in Europe until Leonardo of Pisa (aka Fibonacci) published his ground breaking book Liber Abaci in 1202. By studying the reproduction of rabbits and analyzing the growth of the population over time, Fibonacci was able to observe a breeding pattern unrealistic in most other species. The unique characteristics of the sequence set it apart from all other recursive mathematical series. The first two numbers of the sequence are 0 and 1. All numbers following are calculated by taking the sum of the two previous numbers. Thus the first fifteen numbers of this infinite sequence are the following: {0,1,1,2,3,5,8,13,21,34,55,89,144,233,377}.
How the sequence corresponds to the Golden Ratio is seen by dividing any number in the sequence by the previous number. By doing this you obtain numbers very close to one another and that oscillate around Golden Ratio. In fact after thirteen iterations the numbers becomes fixed (≈1.618) and converge to more and more precise approximations of the Golden Ratio. Next post I will touch on some mind-blowing examples of this pattern in nature.