The unilluminable room problem

Computers & Mobile Science
The unilluminable room problem
Tokarsky Room.jpg

Part of this problem, posed by one Ernst Straus in 1952, is to design a polygonal room lined with mirrors having at least two points such that any ray starting at one point can reflect around the room forever without hitting the other point, and vice versa. One such room, shown above, was demonstrated by George Tokarsky in 1995. It has 26 walls. An improved 24-wall version was produced by D. Castro in 1997.

There are more details, and a cool downloadable demonstrator app, over at Wolfram MathWorld.

Check out George Hart’s Math Monday columns

2 thoughts on “The unilluminable room problem

  1. relawson says:

    I’m immediately reminded of a game of billiards in this shot. Then, I think of those damn games where you have to direct the laser toward a goal using mirrors and stuff. Man I love those!

    This room must have taken a while to design.

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I am descended from 5,000 generations of tool-using primates. Also, I went to college and stuff. I am a long-time contributor to MAKE magazine and My work has also appeared in ReadyMade, c't – Magazin für Computertechnik, and The Wall Street Journal.

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