Tuesday, March 5, 2013

Rooms and Lines and Angles, Oh My

(via Wikipedia)

If you're still catching up on yesterday's material, a lighter read today, but none-the-less interesting, especially for geometers... called "the illumination problem" and goes back originally to the 1950s, but MathFail blog just posted about it:


or, you can just look it up on Wikipedia:


Question is, can you create a room of some shape completely lined with mirrors (but with no interior rooms or closed-off areas) such that a light source could be positioned at some one point, and the light beams therefrom not be observable from some other point in the room space; in short, normally any light source would fill the entire room with light beams -- is there a geometric way to prevent that from happening? (alternatively, the problem is sometimes stated in terms of creating a billiard table such that a ball taking off from one point would never drop into a hole at another point on the surface, even given infinite wall-bounces). Can it be done?...

Yes! (theoretically).

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