Triangular Billiard

Choose a point on a side of a triangle. Imagine shooting a ball from that point parallel to one of the sides of the orthic triangle that meet at the foot of the altitude on that side. Let the ball roll. For some positions of the starting point in an acute triangle the ball will return to the starting point after a six legs journey. It then will repeat the same itinerary. For obtuse triangles and some starting points, an analogous situation occurs with an inscribed 18-gon and 9-gons. If you are lucky you may also glimpse a rare inscribed heptagon (a seven sided polygon.)

(There is a number in the lower left corner of the applet. The number shows the maximum number of legs the trajectory of the ball may consist of. This number could be modified by clicking on it a little off its center line. It's up to the right of the center, down to the left. The ball stops if it gets back to a point it has visited previously. Check the "Stop at beginning" checkbox to ignore all such repeated visits but one (if any) at the starting point.)

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

What if applet does not run?

... to be continued ...

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