Catenary out the window
I hung a rope between two trees for my kids to play on the other day, and when I looked out the window later I saw a catenary graph.
The catenary is a curve describing the shape of a in idealized hanging chain, and looks a lot like a parabola (enough so to trick Galileo). Its equation was determined independently by three people in response to a contest challenge.
I like to think of it as the sum of two exponential functions:
Here’s y = ex and y = e-x
…and their sum