Algebra: Why such a big deal about quadratics?
Amongst the many unanswered questions I had when I was taking algebra in school was, "What’s the fuss about quadratic equations?"
I’ve been watching a Stanford lecture by Keith Devlin titled "The Birth of Algebra" in which he gives a wonderful answer:
"I had a discussion with a couple of people as to why there was this huge focus on quadratics. … The answer is if you’re a practical person, you can do an awful lot in the world with linear equations. Sometimes things change at different rates and linear doesn’t work. The next best thing is quadratics and within a certain range of tolerance, that’s as far as you need to go.
"Even an exponential curve looks quadratic over a small interval. It’s just a reasonably good approximation. Look to a physics book. Classical physics books are full of linear and quadratic equations because that was already difficult enough and good enough for doing an awful lot of things. As physics developed, people realized that there were higher order terms that you needed to take into account, but over reasonable areas of accuracy, that will do.
"Same with computer graphics. You can do almost anything with a computer graphics package that can do straight lines and quadratics. You just put them together in a suitable way: piecewise liner and piecewise quadratic and get all kinds of nice shapes. So [linear and quadratic equations] were extremely useful."
Fantastic explanation.