“Illumination Problem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Illumination Problem

释义

Illumination Problem

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 knowncounterexample 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.

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