Ponytail Math

(via WikimediaCommons & Quinn Dombrowski)

The most recent issue of Chalkdust Magazine (downloadable as a pdf) includes an article on the mathematics of ponytails (because, of course, math IS everywhere ;)

http://chalkdustmagazine.com/regulars/page-3-model/page-3-model-ponytails/

I’ve always liked ponytails (on females), and imagine most guys do; never cared much for pigtails, braids, bouffants, beehives, or a bunch of other contortions women put their hair through, but simple ponytails are coool! And according to the above piece, ponytails have “Rapunzel numbers” that help achieve a wide, bushy effect under the influence of gravity (and yes, there's a specific equation for it)… so read up! 

This got me to wondering if anyone else had looked at ponytails from a mathematical angle. And googling a bit, wouldn’t you know, Keith Devlin addressed the topic for NPR back in 2012:

https://www.npr.org/2012/02/18/147090057/finally-the-physics-of-the-ponytail-explained

Wherein he writes in part:

“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.”

Keith never specifically mentions the “Rapunzel” factor but does conclude that density, elasticity, and curliness, are the 3 hair fiber components to an attractive ponytail.

The abstract for the actual British study Dr. Devlin was reporting on is here:

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.078101

Worth noting too that this study won the Ig Nobel Prize for physics in 2012!: ;)

https://blogs.scientificamerican.com/scicurious-brain/ignobel-prize-winner-in-physics-the-amazing-ponytail/  

Finally, an updated 2017 version of the topic (from one of the original authors, and including plenty of real math) is here:
http://brewminate.com/leonardo-rapunzel-and-the-mathematics-of-hair/

It turns out that even the Wikipedia page for "ponytail" includes a section on the ponytail math/equation:

https://en.wikipedia.org/wiki/Ponytail

Now, if someone would just kindly point me to some mathematical studies of male pattern baldness (sometimes known as the non-hairy ball theorem)…. 

[also, lots more to enjoy in the current issue of Chalkdust, linked to above].