A Multiple Integration Approach to the Broken Stick Problem with Predetermined Minimum Piece Lengths

Abstract

Summary Not many mathematical problems can be successfully introduced around a dinner table or in other social settings, but a quick internet search tells us that broken stick problems are among the classics that still engage. The fact that solutions may require basic knowledge of calculus, probability, and combinatorics helps demonstrate the power and necessity of mathematical formalism. In this article, the general intention has been to show how multiple integrals calculate probabilities in relation to polygons made by pieces from a randomly broken stick of unit length. Most of this article is devoted to proving a probability formula for the case where side lengths have predetermined lower bounds. This formula generalizes a well known corresponding formula without these requirements.