Learn what the Fibonacci sequence is, its relationship to population growth, and how it can make you the life of the party.
Fibonacci vs. Geometric Sequences
So how many rabbits are there after twelve months? Well, if you work it out, the thirteenth Fibonacci number is 233—so 233 pairs is 466 rabbits. (Note that we need to use the thirteenth, and not the twelfth, Fibonacci number because each represents the number of pairs at the beginning of the month. So, the thirteenth number corresponds to the beginning of the first day of the subsequent year—which is exactly what we want.) Clearly, taking into account the fact that organisms can’t reproduce immediately after they’re born has a dramatic effect on the rate of population growth. After 12 monthly doublings, exponential growth from the geometric sequence model we talked about before predicts 8192 rabbits—that’s more than 17 times the number predicted by the Fibonacci sequence! Of course, even the Fibonacci sequence is too simplistic—living beings eventually die, for example. But it’s a beautiful application of how a bit of simple math can model the very complex world. And there’s much, much more it can do too...
Math, Fun, and Fibonacci
You might be wondering: What’s practical about the Fibonacci numbers? For today, my answer may surprise you: nothing. Today’s quick and dirty tip is that you shouldn’t look at math as something that always has to be practical. In fact, at its core, math isn’t practical. It’s a puzzle. Mathematicians don’t sit around doing tediously painful, although perhaps practical, long division problems all day; they make up problems and amuse themselves with them. And, as a result, they often discover really interesting things about the world—all because they allowed themselves to play. The Fibonacci sequence is a great example of that: it’s cool, it’s fun, it’s surprising, it’s beautiful, and if you play your hand right, it just might make you the life of the party.
Fibonacci Numbers in Nature
But what really makes this sequence so famous? Why was it in The Da Vinci Code? What about flowers and shells and the golden ratio? And, speaking of that: What’s the golden ratio? Stay tuned, because in the next article, we’re going to find out. And as for my whole “there’s nothing practical about the Fibonacci numbers”—well, that really was just for today. In truth, there actually are practical uses. We’ll be talking about those things too.
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Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!
Rabbit image from Shutterstock