DISTANCE FUNCTIONS AS GENERATORS OF CHIRALITY MEASURES

A non-numerical analysis is presented of chirality measures associated with a set of topologically equivalent distance functions. A chiralit y measure is defined as the minimum distance that separates a chiral a nd an achiral object (first kind) or two enantiomorphs (second kind). On the basis of this analysis, as applied to triangles in the Euclidea n plane, results of an earlier computational study of the Hausdorff ch irality measure are now fully understood. Analytical proof has been pr ovided for an earlier conjecture, based on a numerical analysis, that the union of enantiomorphous triangles is achiral under conditions of maximal overlap. Geometric parameters for the most chiral triangle, as determined by a family of three measures of the first kind, are found to differ substantially from those determined by the corresponding me asures of the second kind; none of these extremal triangles is degener ate.