One of the world's most beautiful faces is that of Heard. The claim has been recycled for a while now, and recently came up in the wake of Heard's trial.

This claim is based on something.

Heard rates highly on the "golden ratio test". The Golden Ratio is how close a person's facial proportions are to it. It's a formula for beauty.

The Pythagoreans and the Golden Ratio

About 2,400 years ago, the Pythagoreans discovered the Golden Ratio. The Greek symbol represents the mathematical value called "phi".

Many numbers were seen by the Pythagoreans as having mystical, philosophical and ethical significance. The symbol they chose was the pentagrams. It was a sign of health to them.

There is a golden ratio displayed. This is the author's work.

The curious ratio is one of the reasons that quotients are interesting. The four black lines grow by at each step in the picture. The side length is shorter than the horizontal one.

Six circles of the same size are arranged in two rows of three and nestled inside one large circle. The diameter of the small circles is smaller than the large circle's.

The person was represented in circles. This is the author's work.

The golden ratio is related to the famous number sequence. As the numbers get bigger, the ratios between one number and the next get tighter. 13-8, 21-13, 34-21, and so on are examples.

In math, the Golden Ratio is very common. In nature, they create spirals in flowers, pine cones, and the arms of certain galaxies.

There is a sequence of numbers in a flower. There is a picture of L. Shyamal on Wikimedia.

Plato's realm of ideals

Influenced by the Pythagoreans and their love of beautiful math, Greek philosopher Plato proposed the physical world is an imperfect projection of a real realm of truth and ideals. There isn't a perfect triangle in real life.

Plato says that the truths and ideals can only be seen in the physical world through logical reasoning or through order.

Modern science and its presumption of universal laws of nature were influenced by this.

Luca Pacioli was a Renaissance mathematician. The Golden Ratio was covered in a trilogy published in 1509. The first bout of interest in the Golden Ratio was sparked by this work.

The Platonic idea that human bodies should meet certain mathematical proportions was promoted. Da Vinci used this ideal in his illustrations.

The man is Da Vinci. The public domain.

The myth of the Golden Ratio in ancient art

In his books between 1854 and 1884, the author expanded on this idea. All of the most beautiful and fundamental proportions are related to the Golden Ratio, according to his final book. The Golden Ratio was said to be beautiful in ancient Greek art and architecture.

This has been dispelled as a myth according to Mario Livio. Studies show that the Golden Ratio is rarely seen in ancient Greek art and architecture.

The most beautiful building in the world is said to be the Parthenon in Athens. This claim is not true.

The myth is still going strong. The Golden Ratio is used in art, architecture, photography and plastic surgery.

Marquardt's mask

Stephen R. Marquardt is a cosmetic surgeon. Marquardt claimed to have found the Golden Ratio. He said that an ideal face would have a mouth that was twice as wide as the nose.

Marquardt created a face mask that represented ideal facial proportions for the benefit of cosmetic surgeons and orthodontists.

Marquardt's face mask is known as the "repose frontal mask". The name of the company isMBA.

The Golden Ratio test was caused by the mask being used to objectively assess beauty.

The claims of Marquardt have been influential. The Golden Ratio test is used to guide plastic surgery.

The Golden Ratio test debunked

Marquardt measured the facial proportions of movie actors and models. It was his research that led to his claims.

The Golden Ratio test has since been discredited.

It has been shown that Marquardt's mask does not represent sub-Saharan Africans or East Asians.

The facial features of the small population of masculinized European women are represented in this picture. The look is seen in fashion models.

Evidence shows that facial ratios are dependent on biological and cultural factors.

The 2001 and 2015 Miss Universe winners were shown to be strikingly similar. Many cultures see these winners to be very beautiful.

The correlation between their facial ratios and the Golden Ratio of Marquardt's mask was not statistically significant.

There is no magic number that can determine beauty.

Who's the fairest?

Averageness and symmetry, sexual dimorphism, skin texture, emotion and randomness are some of thePlatonic features of facial beauty.

There is no evidence to suggest that the Golden Ratio determines facial beauty.

It's possible to test this yourself. The ratios are :1, 3:2, 1.414:1, 4: and 1:. Is one of these better than the other?

A series of different length rectangles.

Thomas Britz is a senior lecturer at the University of New South Wales.

Under a Creative Commons license, this article is re-posted. The original article is worth a read.