Golden Ratio, Facial Beauty, and Evolution

TWO probably unrelated yet somehow similar news items have popped up recently, so we’ll mention them both at the same time.

The first is reported by BBC News: Perfect face dimensions measured. Here are some excerpts, with bold added by us:

Scientists believe they have worked out the dimensions of the most attractive female face. They say the key to the ideal arrangement of female facial features is the measurements between the eyes, mouth and ears.

Some people have more interesting research projects than others. Continuing:

The study, led by the University of Toronto, appears in the journal Vision Research.

We can’t find the paper yet, but it’s a good story anyway. Here’s more:

Using photoshop, the researchers altered the vertical distance between the eyes and mouth, and the horizontal distance between the eyes in each image. The features themselves never changed, just the distance between them, and the woman’s face was only compared to her own.

Pity the poor devils, toiling away in the lab. So what did these intrepid researchers find?

Following a series of experiments, the researchers came up with the most attractive length and width ratios between features. On length, the distance between a woman’s eyes and mouth should be just over a third or 36%, of the overall length of her face, from hairline to chin. For width, they calculated that the space between a woman’s pupils should be just under half, or 46%, of the width of her face from ear to ear.

There’s more at the BBC article, including some photos — of scientific interest, of course. We know you’ll click over there, so we don’t need to go on with this one.

While we’re discussing biology and geometry, we present you with some excerpts from Mystery of golden ratio explained, which appears at the website of EurekAlert!, the online news service of the American Association for the Advancement of Science (AAAS). The bold font was added by us:

The Egyptians supposedly used it to guide the construction the Pyramids. The architecture of ancient Athens is thought to have been based on it. Fictional Harvard symbologist Robert Langdon tried to unravel its mysteries in the novel The Da Vinci Code.

“It” is the golden ratio, a geometric proportion that has been theorized to be the most aesthetically pleasing to the eye and has been the root of countless mysteries over the centuries. Now, a Duke University engineer has found it to be a compelling springboard to unify vision, thought and movement under a single law of nature’s design.

Also know [sic –known as?] the divine proportion, the golden ratio describes a rectangle with a length roughly one and a half times its width. Many artists and architects have fashioned their works around this proportion. For example, the Parthenon in Athens and Leonardo da Vinci’s painting Mona Lisa are commonly cited examples of the ratio.

Any time we can bring you a news item that mentions the Pyramids, the Parthenon, the Mona Lisa, and The Da Vinci Code, we’re gonna do it. Let’s read on:

Adrian Bejan, professor of mechanical engineering at Duke’s Pratt School of Engineering, thinks he knows why the golden ratio pops up everywhere: the eyes scan an image the fastest when it is shaped as a golden-ratio rectangle.

Bejan has some serious credentials. Here’s his faculty page at Duke: Adrian Bejan. We continue:

The natural design that connects vision and cognition is a theory that flowing systems — from airways in the lungs to the formation of river deltas — evolve in time so that they flow more and more easily. Bejan termed this the constructal law in 1996, and its latest application appears early online in the International Journal of Design & Nature and Ecodynamics.

We looked, but couldn’t find the article online yet. Here’s more:

“As animals developed organs for vision, they minimized the danger from ahead and the sides,” Bejan said. “This has made the overall flow of animals on earth safer and more efficient. The flow of animal mass develops for itself flow channels that are efficient and conducive to survival – straighter, with fewer obstacles and predators.”

One last excerpt:

In numerous papers and books over past decade, Bejan has demonstrated that the constructal law predicts a wide range of flow system designs seen in nature, from biology and geophysics to social dynamics and technology evolution.

Not many scientific laws have their own website. Check it out.

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2 responses to “Golden Ratio, Facial Beauty, and Evolution

  1. retiredsciguy

    Martin Gardner wrote a wonderful essay on the Golden Ratio in his Scientific American column, “Mathematical Puzzles and Diversions”, sometime back in the 1950s. It was reprinted in his second compilation of his columns.

    Besides all the aesthetic properties of the Golden Ratio, the number itself (1.6180339…) has some interesting properties. For instance, it becomes its square by adding 1, and its reciprocal by subtracting 1. That’s just scratching the surface. It pops up in nature all over the place.

    Gardner’s book mentioned a French researcher who claimed to discover that the average ratio of the height of a woman’s navel to her overall height was about 1.618… If that’s actually the case, it’s easy to understand why we find the Golden Ratio proportion so appealing in art.

  2. retiredsciguy

    This is Martin Gardner’s book I was referring to above: The Second Scientific American Book of Mathematical Puzzles and Diversions 1961; reprinted by University of Chicago Press 1987; ISBN 0-226-28253-8 .

    My copy of the original printing is around here someplace; it’s probably still packed from moving.