X-rays of polygons

Abstract

Various results are given concerning X-rays of polygons in ℝ2. It is shown that no finite set of X-rays determines every star-shaped polygon, partially answering a question of S. Skiena. For any n, there are simple polygons which cannot be verified by any set of n X-rays. Convex polygons are uniquely determined by X-rays at any two points. Finally, it is proved that given a convex polygon, certain sets of three X-rays will distinguish it from other Lebesgue measurable sets. © 1992 Springer-Verlag New York Inc.