Index | Problem
Statement | Polygonal Regions |
Bounded
Smooth Regions | The Three Dimensional
Case |

Links to related topics | Glossary
| References

##
The Illumination Problem

The illumination problem has been tentatively traced
back to Ernst Straus in the early 1950's. Two questions were asked:
###
Question 1

Is a region illuminable from every point in the region?
###
Question 2

Is a region illuminable from at least one point in the region?

For smooth regions, both questions were negatively answered. Based
on the properties of the ellipse, Penrose
and Penrose (1958) constructed a region not illuminable from various
points. By modifying this example, Guy
and Klee showed how to construct smooth regions not illuminable from
any point.

For polygonal bounded regions on the other hand, the solution was not
forthcoming. The problem appeared on various

books of unsolved problems (Klee
1979, Klee and Wagon 1991, Croft
and Falconer and Guy 1991). In 1995, Tokarsky

gave a negative answer to the first question by constructing polygonal
regions not illuminable from every point.

The second question is still open.

Index | Problem
Statement | Polygonal Regions |
Bounded
Smooth Regions | The Three Dimensional
Case |

Links to related topics | Glossary
| References