On a conjectured increasing series: Sleeping habits of armadillos

Abstract

The rate of total heat loss of two bodies maintained at constant temperature in a homogeneous conducting medium of low temperature is a function of the distance between the two bodies. Assuming spherical bodies with equal temperatures, this function has been explicitly computed in [4] and its monotonic increase has been verified numerically. In this note we give a rigorous completely elementary proof of this fact, and thus a positive answer to the question raised by M.L. Glasser in [3].