Golden Ratio Observed In Human Skulls

For centuries, Φ has been found in human anatomy for millennia, and in recent decades, it has also been identified in human physiology. The anatomy and evolution of the human skull have been the subject of much research. The Golden Ratio was discovered in the measurements of human skulls but not in those of other mammals. The results might have far-reaching ramifications for anthropology and evolution.

In order to determine if skull form follows the Golden Ratio (1.618… ), Johns Hopkins researchers compared 100 human skulls to 70 skulls from six other animals and discovered that human skull dimensions did. However, the skulls of less related animals such as dogs, two types of monkeys, rabbits, lions, and tigers deviated from this ratio.

“The other mammals we surveyed actually have unique ratios that approach the Golden Ratio with increased species sophistication,” says Rafael Tamargo, M.D., professor of neurosurgery at the Johns Hopkins University School of Medicine. “We believe that this finding may have important anthropological and evolutionary implications.”

Golden Ratio (Φ) in the partition of a line and also of the nasioiniac arc on the human skull. Division of a line into 2 segments such that the ratio of the line (A) to the longer segment (C) is identical to the ratio of the longer to the shorter segment (B). This ratio is 1.618…, known as the Golden Ratio or Φ. In an analogous situation in human skulls, division of the nasioiniac arc (from nasion to inion, NI) by bregma into a shorter frontal arc (from nasion to bregma, NB) and longer parieto-occipital arc (from bregma to inion BI), creates a geometrical relationship in which the ratio of the nasioiniac arc over the bregma-inion arc (NI/BI) coincides with the ratio of the bregma-inion arc over the nasion-bregma arc (BI/NB), both 1.6. The subdivision of the nasioiniac arc by bregma into 2 unequal arcs emulates the geometrical division of a line into the Golden Ratio.

The authors investigated the neurocranium’s dimensions by focusing on the midline calvarial perimeter between the nasion and inion (nasioiniac arc) and its division by bregma into two sub-arcs. The scientists examined 100 human skulls as well as 70 skulls from six other mammalian species and estimated two ratios: 1) the nasioiniac arc divided by the parieto-occipital arc (between bregma and inion) and 2) the parieto-occipital arc divided by the frontal arc (between nasion and bregma). The authors indicate that in humans, these two ratios coincide and approximate (1.64 0.04 and 1.57 0.10). These two ratios were not only distinct but also unique to each of the other six mammalian species.

The gap in the ratios revealed a tendency toward convergence in terms of species complexity. The separation of the nasioiniac arc by bregma into two unequal arcs is comparable to the geometrical division of a line into Φ. The authors propose that the Golden Ratio () concept, which has been seen in other biological systems, may be present in the design and evolution of the human skull.

Mammalian Skull Dimensions and the Golden Ratio, Marco Moscarelli, Tamargo, Rafael J. MD; Pindrik, Jonathan A. MD

Published: September 2019
DOI: 10.1097/SCS.0000000000005610

Source: Mammalian Skull Dimensions and the Golden Ratio (Φ)