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# Illumination problem

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### Illumination problem

Roger Penrose's solution of the illumination problem using elliptical arcs (blue) and straight line segments (green), with 3 positions of the single light source (red spot). The purple crosses are the foci of the larger arcs. Lit and unlit regions are shown in yellow and grey, respectively.

The illumination problem is a resolved mathematical problem first posed by Ernst Straus in the 1950s.[1] Straus asked if a room with mirrored walls can always be illuminated by a single point light source, allowing for repeated reflection of light off the mirrored walls. Alternatively, the question can be stated as asking that if a billiard table can be constructed in any required shape, is there a shape possible such that there is a point where it is impossible to the billiard ball in a at another point, assuming the ball is point-like and continues infinitely rather than stopping due to friction.

The problem was first solved in 1958 by [2] This was a borderline case, however, since a finite number of dark points (rather than regions) are unilluminable from any given position of the point source. An improved solution was put forward by D. Castro in 1997, with a 24-sided room with the same properties.[1]

Solutions to the illumination problem by George W Tokarsky (26 sides) and D Castro (24 sides).

## References

1. ^ a b c
2. ^
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