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Sunday, January 5, 2014

How Honeybees Grow

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Bees. To some they represent the very worst part of any summer day. Me? I'm quite allergic to bee stings, but I no longer discriminate between the different types of bees in my life. I run from them all.

But let's give bees credit. They give us honey, which is delicious. But more than that, as I understand, bees are the key to transferring pollen between flowers. And in pollinating plants and flowers, they represent a key piece in our country's agricultural puzzle. They can also teach us about the Fibonacci sequence.

You see, honey bees reproduce according to an unusual set of constraints. When the queen bee mates with a male, their offspring is a female. These bees are typically known as 'worker bees'. But what makes them interesting is that they always have exactly two parents. Interesting? Don't all animals have two parents? NO!

When a queen bee lays an egg that is not fertilized, that egg becomes a 'drone' bee. They are males and do no work (insert joke about males here). So to simplify, a male (drone) bee has only one parent. But a female (worker) bee always has two parents. If you were to build a family tree for a single drone (male) bee, it would look something like this:

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Do you see what I see? Look on the right side of this image....Fibonacci numbers! How do they work?

The first male bee is just one bee (Generation 1). That male must have a SINGLE parent, and that parent must be a female (Generation 2). But we know that the female must have come from two parents (Generation 3). Now it gets interesting. The female in generation 3 came from two parents, but the male in that generation only had one parent (a female). So in Generation 4, there would be three bees.

Moving on, you can see how each bee in Generation 4 came about. The two females each had two parents, but the male had only one. Therefore, in Generation 5, there will now be five bees. And finally, you can see how in Generation 6, there are going to be eight bees.

1, 1, 2, 3, 5, 8, ...  Fibonacci numbers.

This is where most people being to realize that this sequence is something more than just a mathematical oddity. The rabbit problem was a little contrived, don't you think? But bees are bees. And in the coming posts, we will be exploring some very unusual and unexpected examples of objects in nature that somehow show up as Fibonacci numbers. Stick around - it's going to be an interesting ride!

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