Using model systems to demonstrate instances of mathematical inequalities

By considering certain properties of model systems, one can sometimes demonstrate instances of appropriate mathematical inequalities. For example, by considering the temperature-equalization process in a set of contiguous metal blocks, one can demonstrate instances of the mathematical inequality that states that the arithmetic average of a set of non-negative real numbers is never less than the geometric average of those same numbers. For each of six different mathematical inequalities, an appropriate model system is used to demonstrate instances of the inequality. (C) 1995 American Association of Physics Teachers.