Some Thoughts On Applications Of Polynomials

Elementary applications for the mathematics of polynomials have historically tended to emphasize either the physics of moving bodies or the economics of maximizing profit.

The first is certainly the most popular of examples: A body moving subject to Newton's laws and to constant vertical acceleration will follow a parabolic path, and this leads to beautiful and physically verifiable results as long as acceleration is indeed close to constant.

In the economics example, if we assume that the unit production cost is a linear function of quantity, and that demand is linearly related to price, we again see the usefulness of quadratic functions.

It seems likely, however, that the assumptions in the latter situation, while as simple as possible, are not easily verified "out there."