Introducing the Polynomial

I’ve done as much as I want with piecewise constant interpolations, at least for the moment. The next step that makes sense to me is to look into polynomials. They’re a powerful tool to use in interpolations, but that doesn’t stand out, because they’re powerful tools for most uses. They’re very popular mathematically, since a few polynomials can turn what was a young student’s natural interest in mathematics into a passionate lifelong loathing, with the occasional dream of being haunted by the “quadratic formula”. It’s worth taking a few paragraphs to see what polynomials are, and why they’re popular among those who get past that class.