I remember in 1st grade, not long after having been introduced to numbers by coloring and cutting them out in paper, we were set to draw meshes by systematically connecting inverted points on an angled line using only a straight-edge. The result was a mind-bogglingly curved mesh! Years later I realized we had essentially been constructing quadratic Bézier curves. (But I don't think our teacher knew that, honestly.) https://commons.wikimedia.org/wiki/File:Quadratic_Beziers_in...

My point is that Bézier curves have great bang for the buck. A kid can understand the principle and an adult mathematician/engineer can write a thesis about them. And the curves look equally pretty to both parties. The topic sucks you in!