Some
women and some men with long hair tie it back in a ponytail. When I see a young
woman walking down the street with her ponytail, my attention is drawn to her
face as with the hair drawn back, the bone structure is more clearly visible.
However,
some physicists are drawn to the shape of the ponytail and want to describe it
in the purest poetic terms, that is, in terms of mathematics so that its
essence can be captured by a single number.
Goldstein,
Warren and Ball have been discussing ponytails at length and have come up with
the correct poetry, which they have released on an unsuspecting world via
Physical Review Letters (1).
They
waxed mathematically lyrical about the gravitational force on each hair
producing a tension which is balanced by the restoring force from the
elasticity of the hair along with the local density of hair in the bundle which
forces the hairs to spread apart, an effect which is exacerbated by the average
curliness of the hair.
The
beauty of getting all these forces into perfect balance allows the shape to be
defined by their ratio. That ratio is now called the Rapunzel Number. That
number will go up or down as the hair grows, is cut or is treated with caring
hands anointing it with expensive products.
I’ve
no doubt that many physicist enjoy fairy tails and the tale Rapunzel’s golden
locks hanging down from her tower, but I feel obligated to point out that she
didn’t wear them in a ponytail, but in strong braids.
And
where is Dame Gothell (the enchantress) and the prince in all this?
