Scientific Study Reveals the Human Skull Follows the Golden Ratio Principle

The authors of a new scientific study explain that the Golden Ratio (F) principle, documented in other biological systems, may be present in the architecture and evolution of the human skull.

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The Golden Ratio, described by Leonardo da Vinci and Luca Pacioli as the “Divine Proportion”, is an infinite number that is often found in nature, art, and mathematics. However, the Golden Ratio has been studied and researchers since Euclid, a Greek mathematician, often referred to as the “founder of geometry.”

The Golden Ratio is an irrational algebraic number (its decimal representation has no period) that has many interesting characteristics and was recognized in ancient times, not as an arithmetic expression, but as a relation or proportion between two segments of a line, that is, a geometric configuration.

The Golden Ratio has therefore been found to appear in various geometric figures and in nature: in the veins of the leaves of some trees, in the thickness of the branches, in the shell of a snail, in the sunflower florets, it is also found in pine cones and seashells as well as galaxies and hurricanes. The Golden Ratio is even found embedded within the Great Pyramid of Giza, the only standing wonder of the ancient world.

Golden Ratio Represented in a Seashell. Shutterstock.
Golden Ratio Represented in a Seashell. Shutterstock.

One of its most curious arithmetic properties is that its square (Φ2 = 2.61803398874988 …) and its reciprocal (1 / Φ = 0.61803398874988 …) have the same infinite decimal numbers. Likewise, an aesthetic character is attributed to objects whose measurements keep the golden ratio. Some even believe it has mystical importance. Throughout history, its inclusion in the design of various works of architecture and other arts has been attributed, although some of these cases have been questioned by mathematics and art scholars.

Now, a new study has demonstrated that the Golden Ratio is truly a cosmic phenomenon, found everywhere.

In a new study that looked into whether the shape of the human skull follows the Golden Ratio, researchers at Johns Hopkins University compared 100 human skulls with 70 skulls from six other animals and found that the dimensions of the human skull followed the Golden Ratio.

Golden Ratio (Φ) in the partition of a line and also of the nasioiniac arc on the human skull. John Hopkins University / Journal of Craniofacial Surgery.
Golden Ratio (Φ) in the partition of a line and also of the nasioiniac arc on the human skull. John Hopkins University / Journal of Craniofacial Surgery.

However, the skulls of less related species, such as dogs, two types of monkeys, rabbits, lions, and tigers, diverged from this proportion.

“The other mammals we surveyed actually have unique ratios that approach the Golden Ratio with increased species sophistication,” explained 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.”

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The Golden Ratio can be calculated by taking a line and dividing it into two unequal parts, with the length of the longest part divided by the shortest length equal to the total length divided by the longest part.

The research detailing the discovery has been published in the September issue of the Journal of Craniofacial Surgery.

It is noteworthy to mention that Tamargo’s love for history and anatomy led him in 2010 to publish on finding a human brain and spinal cord in the depiction of God in Michelangelo’s Sistine Chapel painting.