In the early 1950s, Ernst Straus asked
- 1. Is every Polygonal region illuminable from every point in the region?
- 2. Is every Polygonal region illuminable from at least one point in the region?
Here, illuminable means that there is a path from every point to every other by repeated reflections. Tokarsky (1995)
showed that unilluminable rooms exist in the plane and 3-D, but question (2) remains open. The smallest known
counterexample to (1) in the Plane has 26 sides.
See also Art Gallery Theorem
References
Klee, V. ``Is Every Polygonal Region Illuminable from Some Point?'' Math. Mag. 52, 180, 1969.
Tokarsky, G. W. ``Polygonal Rooms Not Illuminable from Every Point.'' Amer. Math. Monthly 102, 867-879, 1995.
© 1996-9 Eric W. Weisstein
1999-05-26