Why Didn't I Know That?

Even if you don't consider yourself a 'math person', it's possible and even likely that you're heard of the Fibonacci sequence. It's one of those things math teachers talk about to try to get kids interested in math, something that crosses the border from mathematics to pop culture on occasion.

For the unfamiliar, the Fibonacci sequence begins with the numbers 0 and 1 (or in some versions, 1 and 1—which ends up, for all practical purposes, making no difference whatsoever). From there, you get the next number in the sequence by adding the previous two numbers together. So the first few terms in the sequence are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597....

The Fibonacci sequence has been linked to things as varied as pine cones, bees, Debussey, "The DaVinci Code", the orbits of the planets, and the Golden Mean. Anciently, some people thought the Fibonacci numbers had mystical properties. I've even used the sequence as the basis of a plot point in a Champions campaign.

I learned something new about the sequence the other day, though. As I was sitting with a junior high school math class in a library presentation, the librarian pointed out that any three consecutive numbers in the sequence share an interesting relationship. Take any number in the sequence and square it. Then take the numbers immediately before and after your chosen number and multiply them together. Then subtract the smaller result from the larger. For example:

55 ² = 3025
34 x 89 = 3026
3026 - 3025 = 1

The difference will always be 1. I never knew that.

It's amazing what you can learn just by being someplace that you normally wouldn't be.