I've seen some yarn art made by stretching the yarn over nails set up like this:
Mathematically, the dark blue curve outside the circle results when you connect the points:
[a, c] and [c, c-a] for some c as a varies from 0 to c (pictured is c=5).
Dr. Rose found the parametric equation for the curve:
The graph of the radius in polar coordinates for this function is:
Which looks a lot like a normal distribution but is too short and wide for what would be the standard deviation. You can see the radius is always greater than 5, so it does indeed lie outside the circle of radius 5.