THE PONYTAIL SHAPE EQUATION. Two months ago I posted about how a physicist had provided a mathematical explanation for an observation made by Leonardo da Vinci. Now, mathematicians have an explanation for another observation by Leonardo. Leonardo observed in his notebooks the way that streamlines of hair resemble the flow of fluid. Now physicists, as this article explains, have developed a mathematical theory that explains the shape of a ponytail. They call it the Ponytail Shape Equation, and there is a quantity in the equation which they call the the Rapunzel Number. The article says the equation “takes account of the stiffness of individual hairs, the effects of gravity and the average waviness of human hair”. The Rapunzel Number is a ratio used “to calculate the effects of gravity on hair relative to its length.” The result has implications for understanding the structure of materials consisting of random fibers, such as wool and fur. (link via Instapundit)

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