Can you recognize the shape of a figure from its shadows
János Kincses, Árpád Kurusa · 1995
. In connection with the Hammer's X-ray picture problem we discuss the following question: Given two convex compact sets inside a circle such that the sets subtend equal angles at each point of the circle, is it then true that the sets must coincide? 1. Introduction In 1961 P.C. Hammer proposed the following question: How many X-ray pictures of a convex body must be taken to permit its exact reconstruction? There are, in fact, two different problems here, according as the pictures are taken from infinity, or from finite points. An X-ray picture of a convex body from a direction (from a point) is defined as a function which for any line parallel to the given direction (passing through the given point) gives the length of the segment in which the line intersects the body. Both cases of Hammer's X-ray problem have nice solutions. In the parallel beam case R.J. Gardner and P. McMullen [3] proved that there are four universal directions such that if any two convex bodies have the same X-ra...