# Astroid as Catacaustic of Deltoid

This image, drawn by Xah Lee, shows a deltoid and its catacaustic. The deltoid is the curve traced by a point on the perimeter of a circle that is rolling inside a fixed circle whose radius is three times as big. It’s called a deltoid because it looks a bit like the Greek letter delta: $\Delta$. The catacaustic of a curve in the plane is the envelope of rays emitted from some source and reflected off that curve.

# Enneper Surface

This is the Enneper surface, as drawn by Greg Egan using Mathematica. It’s a minimal surface, meaning one that necessarily gets more area if you warp any small patch of it. A soap film will make a minimal surface if it doesn’t enclose any air. But the Enneper surface intersects itself: it’s immersed in 3d space, but not embedded. So, you can’t make it with soapy water!