Mixed volume

In mathematics, more specifically, in convex geometry, the mixed volume is a way to associate a non-negative number to a tuple of convex bodies in . This number depends on the size and shape of the bodies, and their relative orientation to each other. Definition Let be convex bodies in and consider the function where stands for the -dimensional volume, and its argument is the Minkowski sum of the scaled convex bodies . One can show that is a homogeneous polynomial of degree , so can be written as