More backwards functions: Unevaluating polynomials (opens in new tab)

Polynomial Interpolation:

Input: a set of points

Output: polynomial that passes through all points of Input

Here, since the input are just two numbers, I don't think it is polynomial interpolation.

That reminds me of the time I rediscovered averaging. I thought I was "inventing" a new type of averaging by imagining masses attached to a massless beam. I started solving for a fulcrum when the torque would evenly balance. I then imagined instead of points, that I had one or more masses distributed continuously along the line, where the mass at any point along the line could be described by the area under a curve. It was only after I realized that I had calculated a centroid for the system, that it donned on me, I was actually calculating the average, as I had first done in elementary school. In short, nothing I was doing was new. I had simply discovered a new way to think about the problem that was not immediately clear when I came up with the thought experiment. In hind sight, it was completely obvious, but not before I ventured into calculus to solve this "tough" problem.