Friday, August 06, 2004

Silly rabbit, tricks are for kids

Ever sit around wondering about Fibonacci numbers? I do. I like the way it sounds. FEEB-OH-NACHI.

Anyway, Fibonacci numbers are everywhere, you know.

So, being a curious type and pretty darn proficient with Web searches I decided to find out a little bit about Fibonacci numbers. A little googling and I dug up the following info:

"Leonardo Pisano is better known by his nickname Fibonacci. He was the son of Guilielmo and a member of the Bonacci family. Fibonacci himself sometimes used the name Bigollo, which may mean good-for-nothing or a traveller. Which leads to the following question:

Did his countrymen wish to express by this epithet their disdain for a man who concerned himself with questions of no practical value, or does the word in the Tuscan dialect mean a much-travelled man, which he was?

(That cracks me up)

In 1225 Fibonacci took part in a tournament at Pisa ordered by the emperor, Frederick II. It was in just this type of competition that the following problem arose:

Beginning with a single pair of rabbits, if every month each productive pair bears a new pair, which becomes productive when they are 1 month old, how many rabbits will there be after n months?
(apparently wondering what the result of lots of rabbits "getting busy" was a burning question in 1225)

Answer to rabbit problem

Imagine that there are xn pairs of rabbits after n months. The number of pairs in month n+1 will be xn (in this problem, rabbits never die) plus the number of new pairs born. But new pairs are only born to pairs at least 1 month old, so there will be xn-1 new pairs.

xn+1 = xn + xn-1

Which is simply the rule for generating the Fibonacci numbers."

Well, duh!

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