An elliptical pool

@StevenStrogatz posed a fun question this evening:

If an elliptical swimming pool has a one-foot wide border around it, is the outer edge of the border also an ellipse?

— Steven Strogatz (@stevenstrogatz) June 28, 2014

People quickly realized the answer is “no,” but how to show it?

I’ll let someone else do the formal proof, but a quick visualization makes it pretty obvious. Play around with the sliders below to see when the border is close to being an ellipse, and when it’s not.

Note: To see the full interactive visualization, you need to download the free CDF player plugin. IE sometimes doesn’t play nice with CDF unless you put the page in “compatibility mode,” so you might want to view this in Chrome.