In 1929, the Anglo-American mathematician, Frank Morley, published and proved a theorem, which subsequently came to bear his name, Morley's theorem, also known as Morley's Miracle. It states:

The three points of intersection of the adjacent trisectors of the angles of any triangle form an equilateral triangle.
I have created an interactive OpenGL demonstration of this theorem, using the JEDI-SDL headers and FreePascal. It's nothing much, just a trifle, really, but you may enjoy it. I've only tested it on Linux, but I reckon it should also work on other platforms that are compatible with JEDI-SDL and FPC. Download the source code from here:

http://www.ludicity.org/files/morley.tar.gz (97.4 KB)

I compile it with the command: fpc -Mobjfpc morley.pp

Here's a screenshot:

http://www.ludicity.org/images/morleyss.png (33 KB)

You can click and drag any vertex of the blue triangle, and the red triangle will always remain an equilateral triangle.