Tomography of convex bodies and inscribed polygons
The X-ray problem posed by \textit{P. C. Hammer} [Problem 2 in Convexity, Proc. Symp. Pure Math. 7, Am. Math. Soc., 498-499 (1963)] has received much attention in recent years, particularly because of its generalization to computerized tomography. The author here extends an early contribution to the subject by \textit{O. Giering} [Bayer. Akad. Wiss., Math.-Naturw. Kl., S.-ber. 1962, 225-253 (1963; Zbl 0115.400)]; he shows that, if K is a planar convex body and \(\ell\) is a line of the projective plane, then there exist three points on \(\ell\) such that the X-rays from these points distinguish K from any other convex body. In the case proved by Giering, \(\ell\) was the line at infinity (giving parallel X-rays).
scientific article; zbMATH DE number 4105740