Think about it:
- they form the equations of rocket science (literally) because they describe the movement of rockets
- they have a focal point which leads to their usage as parabola antennas and headlights
- they are at the heart of parabolic partial differential equations (e.g. the heat equation or Black Scholes equation in finance)
they even have strong connections to stochastic calculus (as an intuition: whereas with standard calculus one has straight lines at the infinitly small, with stochastic calculus one has parabolas)
...and you could build a nifty analog multiplier with it (see here) - I did this with my kids, they loved it and were fascinated by it! :-)
Do you know of other interesting connections, books, articles, links...?