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Monday, July 13, 2015

**Abstract:** If a stick is broken up at two random points, what is the probability that the three pieces will form a triangle? This question, called the broken stick problem, first appeared about 150 years ago in an examination at Cambridge University. It attracted the interest of 19th century French probabilists, and more recently was popularized by Martin Gardner. In this presentation, we consider the generalization of this problem to three (or more) dimensions. In particular, if a stick is broken up at five random points, what is the probability that the six pieces will form a tetrahedron? Questions of this type arise in the field of distance geometry, which has connections to areas such as wireless sensor networks and molecular biology.