Geometry of Human Anatomy


“I hold that the perfection of form and beauty is contained in the sum of all men.” –Albrecht Dürer

In the days before plastic surgery gave us “perfection,” one could argue that artists, mathematicians, engineers, and architects were the experts in the “perfect” human form.

As far back as ancient Egypt, individuals had discovered the mystical properties of the divine proportion, also known as the golden ratio, golden mean, and golden section. Why “divine”? It is considered to be the proportions that constitute anything that is aesthetically pleasing.

The divine proportion ratio is based on phi, which is represented as Φ, the 21st letter of the Greek alphabet. For the mathematicians among us, phi is calculated with the following equation: (1 + √5)/2. For the rest of us who run screaming at the sight of an equation, phi = 1.618. (I never thought I’d need a calculator to write an article.)

Phi’s connection to the divine proportion is based on the relation of three lines: line A, the longest, is 1.618 times the length of line B, and line B is 1.618 times the length of the shortest line, line C. Combinations of the three line ratios are said to be the basis for the divine proportion – the basis for everything perfectly proportional, and thus aesthetically pleasant, in buildings, art, and living things, including humans.

An example of a building designed using this ratio is the Parthenon atop the Acropolis in Athens. In art, the divine proportion can frequently be found, perhaps most famously in the proportions and placement of the participants in da Vinci’s The Last Supper.

But what about the body? The index finger is said to show the ratio: each section of the index finger, moving from the tip to the base of the hand, is larger by approximately 1.618. (1.618 is not a whole number, so the proportions don’t have to be 100% exact, but the closer, the more “perfect.”) Similarly, the ratio of the hand to the forearm is also 1.618.

Who cares about perfection in hands, you say? Well, what about the perfect smile? According to phi-philes, in an aesthetically pleasing mouth, the front two teeth form a golden rectangle (which is said to be one of the most visually satisfying of forms, as it is formed with sides of 1 and 1.618). There is also a phi ratio in the height to width of the center two teeth. And the ratio of the width of the two center teeth to those next to them is also phi. And, the ratio of the width of the smile to the third tooth from the center is also phi.

Or think of da Vinci’s Vitruvian Man (you know, the naked guy standing in a square and a circle). A man with legs and arms outstretched can be inscribed within the perfect geometric figures: a circle and a square. And the ratios can be used to calculate other perfection of humanity, e.g., that the height of a person is the same as the distance from fingertip to fingertip when the arms are outstretched.

And this is not just old belief. Dr. Stephen Marquardt, a former oral and maxillofacial surgeon now engaged in beauty research, has used the divine proportion and some of its relatives, like the golden rectangle, to make a “mask” that he believes is the most beautiful shape a human face can have – even across cultures. The mask is said to fit the faces of several individuals famed for their beauty, such as Marilyn Monroe.

Some real phi-philes even find the ratio a sign of perfect health: that the normal, healthy heartbeat as shown on an EKG beats in a phi rhythm. And more, that a cross-sectional view of the top of the DNA double helix forms a 10-sided figure, made up of two five-sided figures, which have diagonal ratios of 1:1.618. Even the basic building blocks of life have the divine proportion. (Maybe God is sitting back now and laughing at scientists?)

So if you’re visiting your cardiologist, cosmetic surgeon, or dentist, ask how they did in math, and make sure they have a good calculator at hand.

If by now you’re saying “huh?” but suspect there’s something interesting here – or if you understand it entirely and want more information, along with a ripping good yarn, check out The Da Vinci Code by Dan Brown.

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