A Striptease of Entropy

Abstract

Let (p,q) be a point in the truncated unit square]0,1[x [0,1]. The two straight lines connecting (p,q) with (0,0) resp. (1,0) may be considered as the graph of a piecewise linear, unimodal function on the unit interval [0,1] given by

$$f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{q}{p}x for 0 \leqslant x \leqslant p } \\ {\frac{q}{{1 - p}}\left( {1 - x} \right) for p \leqslant x \leqslant 1.} \end{array}} \right.$$

((1))