X-rays of polygons (Q1182992)

The paper deals with the question whether it is possible to recognize star-shaped polygons in the plane when the one-dimensional measures of the sections of this polygon parallel to one or more directions are given. One of the main results says that polygons star-shaped at the origin cannot be determined by \(n\) directions for any \(n\). In contrast to this fact if \(X\)-rays issuing from points rather than from directions (from infinity) are considered, then two points suffice to determine convex polygons. At the last section it is proved that three directions determine convex polygons up to a set of measure zero among measurable sets.