July 15, 2012 - Happy Birthday, Fibonacci!

We don't know if Leonardo Pisano Bigollo (commonly called Fibonacci) was born on July 15, or even on July anything! He probably wasn't. He might very well have been born on my birthday (October 11) or on yours (whatever it may be).

We are not even sure what year he was born! We do know he lived from around 1170 (or so) to 1250 (or so).

Which is a loooooooonnnnnnng time ago.

So why celebrate his birthday, when we don't know when it was? Well, to be perfectly honest, I just wanted to talk about Fibonacci numbers...

Leonardo of Pisa, aka Fibonacci, was arguably the most talented western mathematician of the middle ages. He lived in Italy, but he traveled with his merchant father to what is now Algeria, in Africa, and learned there about the Hindu-Arabi numeral system (which we use today). He traveled all around the Mediterranean Sea to learn from leading Arab mathematicians and then returned to Italy to write down all that he had learned, producing a book called Liber Abaci. Fibonacci is credited with popularizing Arabic numerals in Europe; he pointed out that it is much easier to do arithmetic with these numerals than it is with Roman numerals.

But these familiar numerals are not what I mean when I say “Fibonacci numbers.” This phrase means a number sequence that starts with 0 and 1 and then proceeds with the sum of the previous two numbers.

0 + 1 = 1, so the third Fibonacci number is ALSO 1
1 + 1 = 2, so the fourth Fibonacci number is 2
1 + 2 = 3, so the fifth Fibonacci number is 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13

Do you see that the Fibonacci numbers are starting to get bigger very quickly? They started out so slow:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...

Can you figure out the next several Fibonacci numbers?

And why do we care?

Fibonacci numbers can be seen in nature, from the spiral shells of the Nautilus to branching in trees, from the fruit spouts of a pineapple to the arrangement of a pine cone. Apparently, birds will sometimes even sit according to the sequence!

Chamomile flower with 21 (blue)
and 13 (aqua) spirals marked
so we can easily see them.
21 and 13 are next to each other
on the Fibonacci sequence...
And, it turns out, many Fibonacci-
sequence number pairs are seen
in nature.

Also, computer science uses Fibonacci numbers in search techniques and data structures and so forth.

Wow, that Fibonacci guy was smart, huh?

Well, Fibonacci wasn't the first person to “discover” this sequence. Before Fibonacci's Liber Abaci, this number sequence had already been described by Indian mathematicians. Still, Fibonacci did bring the number sequence to the attention of many, which is why it is named for him.

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