Elliptical swimming pool

A recent Radiolab episode on Numbers had some interesting content, including an introduction to Benford's Law, unfortunately presented as something utterly mysterious and only comprehensible to mathematicians. I don't think it would be too terribly oversimplifying to explain it with dice. If you throw a normal die, the first digit of the results will tend to be evenly distributed among numbers from 1 to 6. A ten-sided or twelve-sided die will favor the initial digit 1. This effect will be even more pronounced with a 20-sided die, which will also show a bit of favoritism toward an initial 2.

There was also a short profile of Paul Erdös, with the first recording I've heard of his voice and that of his biographer, Paul Hoffman.

Somewhere in the story an elliptical swimming pool was mentioned. I thought it was going to be something similar to the elliptical billiard table, with waves instead of balls converging on a focus, but it turned out to be a clever problem. If the elliptical swimming pool has a uniformly wide border around the edge, is the outer edge of the border also an ellipse?