Why Is It Called a Quadratic?

Today I had a really weird experience. I taught a group of students different from any other that I've taught.

Adults.

It was a lot of fun, and something I'd love to do regularly. Adults are just so... reasonable. The best thing about the session is that I got some really interesting questions. Like this one: why is it called a quadratic equation when the highest power is 2, not 4? I'm ashamed to admit I couldn't answer off the top of my head. I had to have a long think about it (and then I googled it, natch).

The reasoning is this: quad in this case doesn't really mean four, it means square. The formula for the area of any quadrilateral will be a quadratic equation, and for every quadratic equation, there exists a quadrilateral whose area is described by it. Similarly, a polynomial of order three is called a cubic not a tresic or something, because it is the formula for the volume of a cube or cuboid.

The pattern breaks down here, because there was no Latin word for hypercube (a four dimensional cube) and they probably weren't too bothered about finding the hyper-volume of one either, so they just called a polynomial of order four a quartic (as in four) and five a quintic, six a sextic, etc.

I know this question has been plaguing you your entire life, so I'm glad to have cleared this up for you! Now go out an enjoy the sunshine whilst it lasts!

Emma x x x