Leonardo, Rapunzel and the Mathematics of Hair

From Leonardo da Vinci to the Brothers Grimm our fascination with hair has endured in art and science. We love it for its "body" or "volume", the fluffiness and elasticity that comes from its random waves and curls. But apart from a purely tactile response, can we take a more quantitative approach to hair, to explain these macroscopic properties in terms of the behaviour of individual hairs? We know that the important physics governing hair involves the interplay of its elasticity, weight, and curliness, but it is only recently that these have been synthesized into a mathematical theory. This talk will cover the mathematics involved, focusing on the important historical developments of elasticity theory due to Euler and Bernoulli and the determination of energy-minimizing shapes through the calculus of variations.