Consider points equally spaced about a circle. Here are 48 such points about a circle of radius 1, in the plane .

Now put another identical circle of points above it in a parallel plane, say at z=1.

Now connect the dots on the top circle with the ones on the bottom circle.

Okay, but don't connect a dot with the dot right beolow it. First turn the top circle through some angle and then connect the dots. Here's an example with . (Actually, we have rotated the top circle and bottom circle in opposite directions through half that amount.)

There's your stringart. Let's see it from the side.

That's it. Now look at the "silhouette" (actually called the envelope of the set of lines). The set of curves on the left and right certainly looks familiar. State and prove a result that explains the shape of these curves. (Hint: Consider the projections of the lines onto the xz-plane, and consider all the lines joining points on the bottom circle to points on the top circle, each turned in opposite directions through an angle .)

A crude, rotatable image is here.