investigates periodic billiard paths in triangles.
McBilliards is a graphical user interface, which allows the user to explore periodic billiard paths in triangles.

McBilliards takes an experimental approach to studying the unsolved problem in Mathematics, "Does every triangle have a periodic billiard path?" That is, given any frictionless billiard table with a triangular shape, can you place a billiard ball (a point mass) on the table and hit it so that eventually it comes back to the same place on the table traveling in the same direction?

McBilliards has facilitated the discovery of many new phenomena related to billiards in triangles. McBilliards continues to evolve, and promises to continue to provide insight into this difficult problem. McBilliards is a web-based Java program which you can operate from a Java-enabled browser. McBilliards also runs as a free-standing Java application. As such, it runs faster and has some C and C++ enhancements which don't work on the web.
(22 Aug 06)- This new McBilliards web page is still under construction. Until it is further developed, please visit one of the older McBilliards websites:
McBilliards can be run as a Java applet inside a browser window. You may choose to run either The standard applet has more features. Consequently, in order to run the standard applet, your browser must download a larger file. This makes the standard version slower to load. Possibly, the basic version is less overwhelming, and thus maybe easier for beginners.

When run as an applet, some more advanced features are disabled (e.g. saving data). See the documentation for other ways to run McBilliards.

Rich has written an applet devoted to the 100 degree result.
How to run McBilliards:
There are two reasonable ways to run McBilliards.
  1. Running McBilliards as an applet:
    See the applets section of this document.
  2. Running McBilliards from your computer:
    McBilliards runs significantly faster when installed on your computer. See the README for instructions.
How to use McBilliards:
  • To appear...
The math behind McBilliards:
  • basic notions [ pdf ]
  • the word window and its objects [ pdf ]
Related Documents:
McBilliards related links:
Supporting Libraries:
Feel free to email the developers: Logo Valid Valid CSS!