ORIENTATION-DEPENDENT CHORD LENGTH DISTRIBUTIONS CHARACTERIZE CONVEX POLYGONS

It is shown that the convex polygons are uniquely determined (up to tr anslation and reflection) by their covariograms. The covariogram can b e represented by the 'orientation-dependent chord length distribution' , i.e. the distribution of the length of chords which are generated by random lines parallel to fixed directions. Thus the result contribute s to answer Blaschke's question about the content of information compr ised in chord length distributions. AMS 1991 SUBJECT CLASSIFICATION: P RIMARY 60 D05 SECONDARY 52 A10; 52 A22