Mammalian Skull Dimensions and the Golden Ratio (Φ)

Rafael J. Tamargo, Jonathan A. Pindrik

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The Golden Ratio (Phi, or Φ=1.618.) is a potentially unifying quantity of structure and function in nature, as best observed in phyllotactic patterns in plants. For centuries, Φ has been identified in human anatomy, and in recent decades, Φ has been identified in human physiology as well. The anatomy and evolution of the human skull have been the focus of intense study. Evolving over millenia, the human skull embodies an elegant harmonization of structure and function. The authors explored the dimensions of the neurocranium by focusing on the midline calvarial perimeter between the nasion and inion (nasioiniac arc) and its partition by bregma into 2 sub-Arcs. The authors studied 100 human skulls and 70 skulls of 6 other mammalian species and calculated 2 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 report that in humans these 2 ratios coincide (1.64±0.04 and 1.57±0.10) and approximate Φ. In the other 6 mammalian species, these 2 ratios were not only different, but also unique to each species. The difference between the ratios showed a trend toward convergence on Φ correlating with species complexity. The partition of the nasioiniac arc by bregma into 2 unequal arcs is a situation analogous to that of the geometrical division of a line into Φ. The authors hypothesize that the Golden Ratio (Φ) principle, documented in other biological systems, may be present in the architecture and evolution of the human skull.

Original languageEnglish (US)
Pages (from-to)1750-1755
Number of pages6
JournalJournal of Craniofacial Surgery
Issue number6
StatePublished - Sep 1 2019


  • Bregma
  • craniometrics
  • golden ratio
  • nasioiniac arc
  • phi
  • skull

ASJC Scopus subject areas

  • Surgery
  • Otorhinolaryngology


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