MathChat

A fly …

Who would think that a mere fly could play a major role in the history of human thought?

But when it comes to the development of Algebra, that’s the story. I’ll explain how this works just a bit later in this blog. But it is all related to what is happening now in algebra classes all around the world.

For it’s spring, that time of year again when we get out the graph paper and the ruler. Kids are working on the Cartesian coordinate plane.

One about I like about the coordinate plane is that there’s an interesting story about how it was discovered, or should I say, invented. [Hard to know the right word for an intellectual Invention like the coordinate plane.]

Anyhow the story goes back to the person credited with the invention of the coordinate plane. That, of course, is René Descartes, who first used an idea similar to the modern coordinate plane in his book, La Géométrie.

According to the story, Descartes was rather sickly as a child, and as a result, he had to stay in bed for days and weeks at a time.

He was also a precocious young mathematician, so while he lay in bed he often thought about math and philosophy.

According to the legend, one day, as young Rene was lying in his bed, sick, he looked up at his ceiling and saw a fly. As he watched the fly, he realized that he could describe the fly’s position by using just two numbers: one number gave the fly’s distance from one wall, measured by a perpendicular from the fly to the wall. The other number gave the fly’s distance from the other wall, again measured by making a perpendicular from the fly to the other wall.

This story is part of the legends of mathematics. We cannot be certain that it is altogether true, and while I have searched, I have not found an unimpeachable source who claims it is gospel. However it is an entertaining story, and there could well be some truth to it.

In his major work, La Geometrie, Descartes analyzes the shape of complex curves by using what were called “reference lines.” While not exactly like the x- and y-axes we use today, these reference lines allowed Descartes to study the properties of curves and to thereby compare one type of curve with another. This is a definite part of math history, as his study of curves is still being published in this book, which you can still find on Amazon.com and many other places. See here for one place to get it.

In any case, I do think that algebra teachers might like to use this story about Descartes, as it shows how just being observant can lead to new perspectives that can have profound impacts. Whether or not this specific story is fully true, the general idea that being observant is a good thing is no doubt as true as ever.