The Golden Ratio, known as the Divine Proportion, is a ratio found in the natural world and countless works of art that’s widely associated with beauty (although, as we'll explain later, most mathematicians really hate this idea). It’s said to be found in the work of Leonardo da Vinci, the architecture of the Parthenon, the shells of marine mollusks, and – according to a new study – the structure of the human skull.
First thing’s first, the golden ratio is an infinite number approximately equal to 1.61803398875. It can be calculated by taking a line and dividing it into two unequal parts, with the length of the longer part divided by the shorter length being equal to the entire length divided by the longer part. It's best known as the pleasing spiral pattern you can see in the image below.
According to a team of neurosurgeons, this ratio can be observed in measurements of the human skull, but not necessarily other animals.
Reporting in the Journal of Craniofacial Surgery, a team of Johns Hopkins neurosurgeons compared 100 human skulls to 70 skulls from six other mammals, including lions, tigers, rhesus monkeys, blue monkeys, dogs, and rabbits.
They measured the skulls and carried out the following calculation: divide the distance from the top of the skull to the back of the skull by the distance from the nasal junction to the back of the skull, and then divide the distance from the nasal junction to back of the skull by the distance from the top of the skull to the back.
In a human skull, these two numbers will give you the ratio 1.6, which, according to their conclusions, is similar to the number 1.618. However, the other species' skulls did not produce such a ratio.
"The other mammals we surveyed actually have unique ratios that approach the Golden Ratio with increased species sophistication," Dr Rafael Tamargo, professor of neurosurgery at the Johns Hopkins University School of Medicine, said in a statement. "We believe that this finding may have important anthropological and evolutionary implications."
Rest assured, while this is an interesting idea, it is likely to annoy a lot of mathematicians out there. That’s because there’s a lot of exaggeration and mumbo jumbo that surrounds the Golden Ratio. As XKCD webcomic points out, you can find this aesthetically pleasing spiral in many images if you try hard enough, it doesn’t necessarily mean they speak to some higher universal ideal of beauty.
“There are lots of ratios and proportions in the human body, but they are not all the Golden Ratio and they are not all precisely the Golden Ratio. It’s a very loosey-goosey, pseudo-science kind of thing that they are promoting,” Eve Torrence, a professor at Randolph–Macon College in Virginia, told The Independent in 2015.
“There’s not this number that’s got this perfection in the way people think it does. It feels dirty to mathematicians. It’s hocus-pocus.”