LONDON (Reuters) – British scientists said on Friday that a “Rapunzel Number” may have helped them to crack a problem that has perplexed humanity since Leonardo da Vinci pondered it 500 years ago.

Scientists from the University of Cambridge and the University of Warwick said they had devised a “Ponytail Shape Equation,” which when calculated using the Rapunzel Number and a measure of the curliness of hair can be used to predict the shape of any ponytail.

Cambridge’s Professor Raymond Goldstein told Reuters that he and his colleagues took account of the stiffness of individual hairs, the effects of gravity and the average waviness of human hair to come up with their formula.

The Rapunzel Number provides a key ratio needed to calculate the effects of gravity on hair relative to its length.

“That determines whether the ponytail looks like a fan or whether it arcs over and becomes nearly vertical at the bottom,” Goldstein said in a telephone interview.

The research also took into account how a bundle of hair is swelled by the outward pressure which arises from collisions between the component hairs.

Scientists said the work has implications for understanding the structure of materials made up of random fibers, such as wool and fur and will have resonance with the computer graphics and animation industry, where the representation of hair has been a challenging problem.

“Our findings extend some central paradigms in statistical physics and show how they can be used to 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 said.

The research was conducted by Goldstein, Professor Robin Ball from the University of Warwick and their colleagues. It will be presented to the American Physical Society in Boston on February 28.

(Reporting by Li-mei Hoang, editing by Paul Casciato)

<span class="articleLocation”>(Reuters) – The mystery of Earth’s missing heat may have been solved: it could lurk deep in oceans, temporarily masking the climate-warming effects of greenhouse gas emissions, researchers reported on Sunday.

Climate scientists have long wondered where this so-called missing heat was going, especially over the last decade, when greenhouse emissions kept increasing but world air temperatures did not rise correspondingly.

The build-up of energy and heat in Earth’s system is important to track because of its bearing on current weather and future climate.

The temperatures were still high — the decade between 2000 and 2010 was Earth’s warmest in more than a century — but the single-year mark for warmest global temperature was stuck at 1998, until 2010 matched it.

The world temperature should have risen more than it did, scientists at the National Center for Atmospheric Research reckoned.

They knew greenhouse gas emissions were rising during the decade and satellites showed there was a growing gap between how much sunlight was coming in and how much radiation was going out. Some heat was coming to Earth but not leaving, and yet temperatures were not going up as much as projected.

So where did the missing heat go?

Computer simulations suggest most of it was trapped in layers of oceans deeper than 1,000 feet during periods like the last decade when air temperatures failed to warm as much as they might have.

This could happen for years at a time, and it could happen periodically this century, even as the overall warming trend continues, the researchers reported in the journal Nature Climate Change.

“This study suggests the missing energy has indeed been buried in the ocean,” NCAR’s Kevin Trenberth, a co-author of the study, said in a statement. “The heat has not disappeared and so it cannot be ignored. It must have consequences.”

Trenberth and the other researchers ran five computer simulations of global temperatures, taking into account the interactions between the atmosphere, land, oceans and sea ice, and basing the simulations on projected human-generated greenhouse gas emissions.

These simulations all indicated global temperature would rise several degrees this century. But all of them also showed periods when temperatures would stabilize before rising. During these periods, the extra heat moved into deep ocean water due to changes in ocean circulation, the scientists said.

(Reporting by Deborah Zabarenko in Washington, editing by Chris Wilson)