Physicists unlock the mathematical secrets of the ponytail

Monday, 13 February 2012 14:47

News & Events - Engineering News

February 13, 2012

While the ponytail may be a ubiquitous hairstyle favored by those on the run, its simple elegance belies its complex mathematical shape, scientists said recently.

Hair has long fascinated scientists who have marveled at how as each strand eloquently falls with seeming ease to form a multitude of hairstyles, shapes and textures. Physicists at Cambridge University said recently they had successfully quantified the curliness of human hair and developed a mathematical theory they contend explains the shape of the ponytail.

PhysOrg reports that the scientists published their findings in Physical Review Letters on Monday. The new theory will help improve the understanding of how human hairs fall in a ponytail, and it could have far-reaching applications, experts said. The Ponytail Shape Equation - as the scientists dubbed their novel formula - uses the stiffness of hair, the effects of gravity and the presence of curliness and waviness to calculate how strands are distributed in the ponytail, according to the researchers.

Cambridge University complex physical systems professor Raymond Goldstein said that although the equation is "remarkably simple," it could help scientists better understand natural materials such as wool and fur. Moreover, he said that the enhanced understanding of the ponytail's underlying mathematical principles could help "solve a problem that has puzzled scientists and artists ever since Leonardo da Vinci remarked on the fluid-like streamlines of hair in his notebooks 500 years ago."

Goldstein and University of Warwick professor Patrick Warren led the team of scientists, the BBC reports. They noted in their findings that the ponytail is swelled by the outward pressure that results from the interaction among the hairs that compose it. Goldstein contended that the Ponytail Shape Equation could be used in conjunction with the aptly named Rapunzel Number to predict the shape of any ponytail.

"To be able to reduce this problem to a very simple mathematical form which speaks immediately to the way in which the random curliness of hair swells a ponytail is deeply satisfying. Physicists aim to find simplicity out of complexity, and this is a case in point," Goldstein added. "We imagine that at least half of the population has direct experience with the properties of ponytails, and we all have likely wondered about the fluffiness of hair."

Goldstein plans to present the research at the American Physical Society's March meeting, which is slated to take place in Boston at the end of the month.