## ‘Rapunzel Number’ Lets Scientists Predict Ahape of Any Ponytail – Solving a Problem Posed by Leonardo da Vinci

Mathematicians may have come up with a ‘Rapunzel Number’ that can predict the shape of any ponytail – solving a problem that has perplexed hairdressers since Leonardo da Vinci posed it 500 years ago.

The equation, which balances gravity versus the ‘springiness’ of hair to predict whether ponytails will be fan-like or pointed, was ‘surprisingly simple’, say the researchers.

The researchers found the number by photographing large bundles of human hair and analysing the maths

The researchers from the University of Cambridge said they had devised a ‘Ponytail Shape Equation’, which when calculated using the Rapunzel Number and a measure of the curliness of hair can be used to predict the shape of any ponytail.

Cambridge’s Professor Raymond Goldstein said he and his colleagues took account of the stiffness of individual hairs, the effects of gravity and the average waviness of human hair to come up with their formula.

The Rapunzel Number provides a key ratio needed to calculate the effects of gravity on hair relative to its length.

‘That determines whether the ponytail looks like a fan or whether it arcs over and becomes nearly vertical at the bottom,’ Goldstein said.

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