Details

Snapshot 1: the oval is made up of six elliptical arcs, representing the six regions formed by extending the line segments joining each nail (not counting the triangle formed by the three nails, in which none of the arcs fall)

Snapshot 2: if the three nails fall on the same line, or any pair of nails fall on the same point, the result is an ellipse; just as all nails falling on the same point results in a circle

Snapshot 3: if there is no slack in the loop of string, the figure is a triangle

M. Gardner, "Fun with Eggs, Part II," The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications, New York: Copernicus, 1997 pp. 59–66.