Probability of random paths across elementary geometrical shapes

Abstract

There are several practical situations where one requires the statistical properties of the straight path length l across a specified geometrical shape. Typical examples are the length of the path of a gamma-ray to the wall of a nuclear reactor (Primak (1956)), the length of a sound ray in a room from one reflection to the next (Kosten (1960)), or the length of a straight path across a square (Horowitz (1964)).