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Solved! The mysterious math of ponytails

Tying your locks in a ponytail is easy, but scientists and artists have puzzled over hair for centuries. Now it's a simple equation.

String theory: Hair has vexed scientists and artists for centuries.
Tim Hornyak/CNET

Does your coif suffer from orientational disorder? Have you checked the gravitational effects on your locks lately? Can you solve the differential equation in your beehive?

Well, scientists now can. Pioneering British researchers have succeeded in formulating an equation that unravels the deep physics mysteries of that great frontier of science, human ponytails.

In a study that screams Ig Nobel Prize, the researchers from the University of Cambridge, the University of Warwick, and Unilever published a hirsute equation that for the first time describes how hairs hang together and predicts the form of a ponytail.

"We identify the balance of forces in various regions of the ponytail, extract a remarkably simple equation of state from laboratory measurements of human ponytails, and relate the pressure to the measured random curvatures of individual hairs," Raymond Goldstein, Robin Ball, and Patrick Warren write in Physical Review Letters.

You'd think these boffins went a-hunting for ponytails in the wild and examined specimens back in the lab. That was probably too hairy a prospect.

Instead, they obtained commercial human hairpieces and measured the random curvature of small samples of hair. They fashioned various ponytails about 10 inches long and noted the average shape.

The data were used to formulate the Ponytail Shape Equation. It takes into account the forces of gravity, "orientational disorder," elasticity, and swelling pressure coming from hair curls.

When used with a variable called the Rapunzel Number, the equation accurately predicted how the ponytails changed shape as they were shortened.

The math could help improve the challenge of realistically depicting hair and fur in animation and video games. Furthermore, it may improve understanding of fiber behavior in biology and industry. Expect a deluge of math-hair ads from shampoo makers too.

I would love this new insight to help out with receding hairlines, but that's probably wishful thinking.

Goldstein will discuss the group's findings at the American Physical Society meeting later this month.

(Via BBC News)