Stephmo has a great weekend on tap
I’m reading another book right now to get it back to the library before the weekend is up and with a lot of other things, the girl is a bit of a math savant. So she discusses Fibnaccis – numbers that are in this math sequence:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987
If you can’t see the pattern right off, this is the formula:
x_n+1 = x_n + x_n-1
And if that doesn’t help (it didn’t help me), this is what these numbers do (other than relax the character in the book by thinking about them):
The first two numbers are 0 and 1 – you add them together and get a sum of 1. You add that second number to the sum and you will then get 2. And you continue – so the chain at first looks like this:
0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
21 + 34 = 55
34 + 55 = 89
55 + 89 = 144
I of course think this is an entertaining parlor trick, but now I’m wondering why this list is named after a guy – well, it turns out these numbers are described as the Golden Ratio. It was also the way to solve this problem:
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, algebra tournaments were very popular back in Fibonacci’s day. The formula also had to take into account that new rabbits couldn’t breed for a month – so this is where his sequence came into play. And then it turns out that it applied not only to rabbits, but to all sorts of things in nature – this is the golden ratio. Petals on flowers, pine cone rows, chambers in various fruits, all sorts of things – followed this sequence.
And as numbers get really large in math, there’s this sort of desire to know which of the bigger numbers you might run across is, in fact, one of these Fibonacci Numbers.
I didn’t take a lot of math – it ended after college algebra and statistics courses – but parts of it does fascinate me. If it had all been interesting trivia where I could scratch the surface, I might have been more drawn to it. :)



