A width-diameter inequality for convex bodies

AbstractA special case of the Blaschke-Santaló inequality regarding the product of the volumes of polar reciprocal convex bodies is shown to be equivalent to a power-mean inequality involving the diameters and widths of a convex body. This power-mean inequality leads to strengthened versions of various known inequalities

An end to gender display through the performance of Housework? A review and reassessment of the quantitative literature using insights from the qualitative literature

The similarity of two convex polyhedra A and B may be calculated by evaluating the volume or mixed volume of their Minkowski sum over a specific set of relative orientations. The relative orientations are characterized by the fact that faces and edges of A and B are parallel as much as possible. For one of these relative orientations the similarity measure is optimal. In this article we propose and test a method to reduce the number of relative orientations to be considered by using geometric inequalities in the slope diagrams of A and B. In this way the time complexity of O(n6) is reduced to O(n4.5). This is derived, and verified experimentally.

Mixed Volumes and Slices of the Cube

AbstractWe give a combinatorial interpretation for the mixed volumes of two adjacent slices from the unit cube in terms of a refinement of the Eulerian numbers