- “Why do people like symmetric things?
- What’s a cardioid?
- Why does the Fibonacci sequence show up in plants?
- What makes e so special?”
There aren’t unequivocal answers to the first and third ones, but some speculations are more reasonable than others….
In the first one, we got into the golden ratio as well as the observation that people find slightly asymmetric faces more attractive than photoshopped symmetric ones.
The challenge of explaining that e^x is its own derivative to someone who is just now plotting points, not functions, was…interesting. I started with the rate*time=distance standby as exemplified in a trip between Houston and Dallas. Then we talked about the difference between average and instantaneous speed. Then we got into plotting (which was a conceptual leap for someone who hasn’t plotted functions). Then speed as the change in position vs time expression, and then the final moment: “e is the only function where the speed graphs and the position graphs superimpose.” A little oversimplified, but not a bad explanation for someone in fifth grade, I think…