Numbers are neat...where you may OCT 17 1999
Numbers are neat...where you may see God, I see mathematics and physics. Whilst reading Fermat's Last Theorem : Unlocking the Secret of an Ancient Mathematical Problem this weekend, I came across my old friend, the Fibonacci sequence. The sequence begins thusly: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34,... and so on, ad infinitum. Each number in the sequence is the sum of the previous two numbers.
But while they may not look special, the Fibonacci numbers have some really unique properties. For instance, as the sequence progresses, the ratio of two successive numbers in the Fibonacci sequence moves towards a special number in mathematics called the Golden Section. Exercise: divide one by the the Golden Section (approximately equal to 1.6180339887) on your computer's calculator and see what you get. Neat, huh?
The Fibonacci numbers also show up in nature. Leaves on branches are separated by distances that correspond to the numbers in the Fibonacci sequence. In many flowers, the number of petals are Fibonacci numbers (black-eyed susans have 21 petals). Why does nature follow the sequence so precisely? It's that pesky Golden Section again and how it relates to the packing of seeds in plants.
Most of the links above go to the excellent Fibonacci Numbers and the Golden Section Web site. Wow, talk about comprehensive. Warning...if you are at all interested in mathematics, you'll be lost at this site *for hours*.
Also, for the more adventurous folks out there, here's all the nasty mathematics of the Fibonacci sequence.
Note to Mouser, if you're listening...isn't 1/the Golden Section ((sqrt of 5 - 1)/2) equal to the packing fraction for spheres (or circles?) that we used when working with glasses? Weird.