SUMMARYThe relationship between the inflection point count on a representative microsection and the integral‐asymptotoic line curvature of saddle surface in the system constitutes a new fundamental stereological equation. While the geometric meaning of this quantity cannot be readily visualized, it is unambiguous, and general for all structures. Combinations of the inflection point count with other descriptors of two‐dimensional structures provide potentially useful descriptors of particle roughness, scale, and some aspects of shape. Like all measures of boundary properties, the inflection point count is sensitive to resolution; it is thus essential to report the level of resolution in conjuction with any experimental determination o