Volume 7, Issue 2
June 1998

Choose three points at random inside a unit square.  What is the expected area of the resulting triangle?  The expectation value is given by an integral over the six-dimensional unit cube.  This article shows how to compute the integral by partitioning the domain into 496 subregions and using a custom integration function.

(If you don't have a copy of Mathematica, you can view the notebook using Mathematica Player.)

Michael Trott studied physics at Humboldt University in Berlin from 1981 to 1986. He received his Ph.D. in theoretical solid-state physics in 1990 from the Technical University of Ilmenau. In 1994 he joined the Research and Development team at Wolfram Research, Inc. His current scientific interests are visualization in mathematics, elliptic functions, the application of computer algebra to physics, and the foundational problems of quantum mechanics.