Finally, The Physics Of The Ponytail Explained Scientists in Britain have been trying to determine whether the shape of a ponytail can be deduced from the properties of a single hair. Host Scott Simon talks with Weekend Edition Math Guy Keith Devlin about a new, soon-to-be-published study that has the answer.

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#### Finally, The Physics Of The Ponytail Explained

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SCOTT SIMON, HOST:

There's an article by three British scientists in the scientific journal Physical Review Letters that says, in part: A general continuum theory for the distribution of hairs in a bundle is developed treating individual fibers as elastic filaments with random intrinsic curvatures, applying this formalism to the iconic problem of the ponytail. The iconic problems of the ponytail? Where's the problem? Who better to explain than our math guy, Keith Devlin of Stanford University?

Keith, this is for real?

KEITH DEVLIN, BYLINE: Yeah, this one caught my eye, too, Scott. I couldn't believe it. Two of the authors are actually classical, sort of research mathematicians and scientists - one at the University of Cambridge, one at Warwick University. The third author is a research scientist at Unilever.

And, of course, Unilever makes hair care products. And we're talking about a \$40 billion global market in shampoos and conditioners. So they got some mathematicians to come up with a mathematical formula to understand how to make more attractive ponytails so that the ponytail curves around in a beautiful, sexy, attractive arc, rather than just hanging limply. That's a \$40 billion question.

SIMON: Keith, is there something to be learned here that pertains to something other than ponytails?

DEVLIN: Yeah, a ponytail is just made up of many individual hair fibers. So the mathematical question is: how does the shape of that fiber bundle derive from the individual properties of the fibers. Now, there's lots of other things that are made up of fibers. There's fiber optic cables, which are of major importance now in communications transmission. The cables that hold up suspension bridges consist of many strands of steel that are bundled together.

So we're talking about mathematics that holds up the Golden Gate Bridge, mathematics that tells us how fiber optic cables behave when they're twisted and bent through conduits. So this is actually much more than a question about hairstyle.

SIMON: So what's the key to having a fuller, flouncier ponytail, mathematically speaking?

DEVLIN: I guess Unilever would like the answer to be: we buy their products. But it comes down to those three factors of the individual hairs that are important. One is its elasticity, one is its density, and one is its curliness. Now, Unilever can't do much about the density, but they could make products that affect the elasticity and the curliness. And so they now know with some accuracy how to affect individual hairs so that the ponytail that someone puts together looks more attractive.

SIMON: Keith, we've known each other for a few years. I'm just going to bet that you're the kind of guy out there in the Bay Area who at one or more points in your life had a ponytail.

DEVLIN: I did. It was a fairly short stubby one. So I wouldn't have benefited from this mathematics.

(SOUNDBITE OF LAUGHTER)

DEVLIN: I never got one of those long ones which would've actually been beneficial - which would've benefited by this new mathematical formula.

SIMON: Keith Devlin, our math guy - I can't believe it, our math guy - speaking with us from the studios of Stanford University.

Thanks, Keith.

(SOUNDBITE OF LAUGHTER)

DEVLIN: My pleasure, Scott.

SIMON: This is NPR News.