Can We Do Without the Hairdresser? A Mathematical Solution

The Germanic folk tale “Rapunzel,” popularized by the Brothers Grimm in 1812, tells the story of a young woman who lets down her hair from a tower window, allowing a prince to climb up and visit her. But is such a situation realistic? Could someone’s hair actually grow that long? This article investigates, using mathematics, what would happen if a person decided to stop cutting their hair. Specifically, we introduce a stochastic model for hair growth and examine how the average length evolves as time tends to infinity. Besides offering curious insights about our hair, the proposed model provides an engaging and unconventional exercise in probability. It can also serve as an innovative way to introduce students and young researchers to the fascinating world of stochastic processes, particularly the Poisson process and renewal theory.