This surface shows that the **Plateau Problem** can well have a **continuum** of solutions: in this particular example (due to **Frank Morgan**, *A smooth curve in R^3 bounding a continuum of minimal manifolds, Archives Ration. Mech. Anal. 75 (1981) 193-197.*), the boundary is made of 4 coaxial circles. The **boundary is rotationally symmetric**, while the
**surface is not**: by rotating, there are **uncountably many solutions** to the Plateau problem! Of course, this particular minimal surface is not area-minimizing.

**Controls:** Move **mouse with left button or A key pressed** to rotate.
Move **mouse with middle button or S key pressed** to zoom.
The checkbox **Show half** highlights the construction of this surface: in his paper, Frank Morgan starts with the least-area soap film spanning the contour shown in the model (a circle and two half circles connected by two line segments). His example is then obtained by adding a second copy of the same
soap film, rotated 180º around the line segments: by Schwarz reflection principle the two surfaces fit together to form a larger minimal surface bounded by 4 circles. The two halves are painted in different colors by checking the box **Two colors** (of course, **Show half** must be unchecked...)

The checkboxes**Show mesh** and **Show smooth surface** are self-explanatory: by default, both are checked.
The button **Change background** cyclically changes the background among a few choices. The default background is flat, but less demanding in terms of graphics resources...

**Webgl applet built with the library three.js (released under the MIT license). This applet is (C) 2012, Sisto Baldo** and is released under GPL. Model computed with Ken Brakke's **Surface Evolver**.

The checkboxes