Saturday, May 5, 2012

Fibonacci Day: Two Fun Facts

Today is Fibonacci day! It is the fifth of May, and five is a Fibonacci number.

As you may know already, I am hosting the Tau 2000 fundraiser for the Bethel Public Library tomorrow, and I am extremely busy practicing my memorization of 2000 digits of the number tau.

I usually do something that is involves some thinking to appreciate the coolness of the proof, trick, pattern, or other mathematical fun fact. However, since I am very busy, I am going to write about a few things that are just quick fun facts about Fibonacci numbers.

Several months ago, we discussed what happens when you square Fibonacci numbers. Now, I'd like to do something similar: see if there are any that are already square. Let's go through.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6725, ...

On this list, there are only three - all towards the beginning of the list. They are 1, 1, and 144. Is there anything interesting about that?

In fact, there is. These three numbers are the only square Fibonacci numbers that exist. Since I don't know how to prove this, I can't, but I'm sure it involves some very complicated math that I wouldn't understand, since I wouldn't know where to begin.

Here is another fun fact. For school subjects, math is commonly applied in science and social studies (dates, coordinates, etc.), but very seldom in language arts. This is a very cool way to relate poetry with Fibonacci numbers, two seemingly different topics.

Take a limerick, which goes something like this:

di dum di di dum di di dum
di dum di di dum di di dum
di dum di di dum
di dum di di dum
di dum di di dum di di dum

How many syllables are in each line? Coincidentally enough, each word is one syllable, which makes it easy to count.

di dum di di dum di di dum   = 8
di dum di di dum di di dum   = 8
di dum di di dum                   = 5
di dum di di dum                   = 5
di dum di di dum di di dum   = 8

Is there any pattern in those numbers? In fact, there is; they are all Fibonacci numbers! Not only that, but there are 3 eights and 2 fives, and both 3 and 2 are Fibonacci numbers. It gets better! If you add up the total number of syllables, you get 34, a Fibonacci number.

We can take it even further! There are 5 di's and 3 dum's in each of the eight syllable lines - both Fibonacci numbers. In the five syllable lines, there are 3 di's and 2 dum's - two Fibonacci numbers again. There is a total of 21 di's and 13 dum's - and those are Fibonacci numbers. Though you wouldn't think it, limericks are filled with Fibonacci numbers. I thought that this was pretty cool!

Answer: A month ago, I gave you the giraffe puzzle:

To make the other giraffe, you must move its back leg over and make it parallel with the body. Then, you just rotate the picture clockwise, and you have it. At the end, it will look like this:

If you solved it, congratulations. It is another puzzle that is so simple that it's hard, which are usually the fun kind.

1 comment:

  1. Wow! 2000 digits of tau! Hope that went well. I'm hard at work memorizing e, pi, and sqrt(2) to get myself on the world ranking list: Don't think they have a tau world ranking list yet, shame though 2000 is very impressive!