In the 12th century, Leonardo Bonacci (a.k.a. Leonardo of Pisa, Leonardo Pisano Bigollo, Leonardo Fibonacci) wrote in Liber Abaci of a simple numerical sequence that is the foundation for an incredible mathematical relationship behind phi. This sequence was known as early as the 6th century AD by Indian mathematicians, but it was Fibonacci who introduced it to the west after his travels throughout the Mediterranean world and North Africa.
Starting with 0 and 1, each new number in the sequence is simply the sum of the two before it.
Starting with 0 and 1, each new number in the sequence is simply the sum of the two before it.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
The ratio of each successive pair of numbers in the sequence approximates phi (1.618...), as 5 divided by 3 is 1.666..., and 8 divided by 5 is 1.60.
No need to get overly stressed-out with mathematics, irrational numbers and such. Soak in some visual goodness;
The Golden Ratio in Nature by Cristobal Vila:
https://www.youtube.com/watch?v=Pp6D-xhJr4A
Fibonacci, PHI, World's most mysterious number, Golden number (crap resolution, but highly educational):
https://www.youtube.com/watch?v=03uC9bhX0Rc
I intend to highlight Mr. Da Vinci in another entry, but I couldn't resist Lisa when it came to this topic.
More food for thought;
15 Uncanny examples of the Golden Ratio in Nature:
http://io9.gizmodo.com/5985588/15-uncanny-examples-of-the-golden-ratio-in-nature
Nature, The Golden Ratio, and Fibonacci too:
https://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.html
Wiki goodness:
https://en.wikipedia.org/wiki/Golden_ratio
https://en.wikipedia.org/wiki/Fibonacci
Super math nuts only:
http://www.friesian.com/golden.htm
