# Decoding the Math Behind Beauty

- Kevin Naruse
- January 4, 2018

More than five centuries ago, Leonardo Da Vinci tried to approximate the ideal in human

beautywith his Vitruvian Man. Da Vinci’s simple sketch makes a radically-sweeping implication: that there are architectural principles behind human beauty that can be investigatedscientificallyanddefinedmathematically.

“*The height of the man is in golden proportion from the top of his head to **his navel and from his navel to the bottom of his feet. The Vitruvian Man **illustrates all of the divine proportions within the human being*”

http://mathcentral.uregina.ca/beyond/articles/Art/DaVinci.html

He called it the Golden Mean. He used this proportion in all of his paintings, including Mona Lisa.

**So what exactly is this ratio or number?**

## The Golden Ratio or Phi

**a/b = (a+b)/a**

Leonardo Da Vinci has long been associated with the golden ratio, reinforced in popular culture by Dan Brown’s 2003 best-seller, The Da Vinci Code. The plot contains pivotal clues involving the golden ratio and a series of numbers known as the Fibonacci series.

http://www.goldennumber.net/leonardo-da-vinci-golden-ratio-art/

This concept has already been explored in the popular media, in discussions about the shape of seashells, the proportion that plastic surgeons use in their practice, the recurrent underlying morphology of flowering plants, and the bodily proportions of many animal species. Now, this same golden ratio is being used to predict the behavior of stars and galaxies in deep space.

Can there possibly be a scientific way to break down physical beauty into a mathematical formula, or secret sacred ratio? Can such a thing be discovered, as well as proven? Might cosmetic surgeons indeed construct truly beautiful faces based upon this knowledge, and for computers to predict, as well as create, what is beautiful?

As fantastical as the notion sounds, and as outlandish as the claim may seem, if there were a real magical formula behind beauty, I became determined to find out if there was any real science behind it.

## The Pentagram, the Fibonacci sequence, and The Golden

Ratio exposed

“A woman’s face is said to be most attractive when the space between her pupils is just under half the width of her face from ear to ear. Experts also believe the relative distance between eyes and mouth should be just over a third of the measurement from hairline to chin.”

– Florence Colgate is ‘Britain’s Most Beautiful Face:’ What Makes Her Face So Perfect?

If you Google terms such as “the Golden Mean” you will see that there is much written about it already. Typing in the keywords “**the math of beauty**” returned nearly sixty million results.

About 58,400,000 results (0.43 seconds)

“The proportional beauty theory has been around ever since Da Vinci applied visionary thinking and mathematical genius to describing the perfect face more than half a millennium ago.”

My interest in the magic ratio of beauty was heightened by an article in the UK-based Guardian, about a competition to find “Britain’s Most Beautiful Face.” The result of an actual competition that took place among eight thousand women in April. There is nothing unusual about a major media outlet would picking up a piece of this kind. It sensationalizes and romanticizes a subject with universal appeal, “nature’s secrets to beauty,” but it did raise an interesting question: how much of it is psychology or biology, how much of it mere idle speculation, and how much is based on real geometry?

If anyone created the idea, it would be Pythagoras, one of the great figures from Greece’s golden age. The famed mathematician and author of the famed Pythagorean Theorem that we all studied in high school geometry.

Pythagoras believed that there was a sacred geometry underlying all of existence, observable patterns in nature which manifest themselves in the flight of bees, the formation of clouds, and the distribution of planets around stars.

According to Pythagoras, “in architecture and design … the shapes people found most pleasing were those whose sides were related by the so-called golden ratio.”

He wasn’t the only thinker among the ancient Greeks who believed this.

So what does all this have to do with beauty, you may ask?

In music, Pythagoras showed that the notes of the musical scale were not arbitrary, but reflected by the tones produced by a lute string when its length was subdivided

precisely into such **simple ratios as 2:1 or 3:2**.

“The magical proportions gave us the facades of the Parthenon and Notre Dame, the

face of the Mona Lisa, the Stradivarius violin, and the iPhone.”

http://www.scientificamerican.com/article/strange-stars-pulsate-according-to-the-golden-ratio/

## Are the Secrets Really in the Stars?

Many well-known artists have emulated the divine proportion in their works.

Salvador Dalí , influenced by the works of Matila Ghyka, explicitly used the golden ratio in his masterpiece, The Sacrament of the Last Super.

Finally from Wired Magazine, I had to mention this:

“MATHEMATICAL CONCEPTS can be difficult to grasp, but given the right context they can help explain some of the world’s biggest mysteries. For instance, what is it about a sunflower that makes it so pleasing to look at?” In Golden Meaning, a new book from London publisher GraphicDesign&, fifty-five designers aim to demystify the golden ratio using clever illustrations and smart graphic design.”

Mario Livio (born 1945) is an astrophysicist and an author of works that popularize science and mathematics. He is currently an astrophysicist at the Space Telescope Science Institute , which operates the Hubble Space Telescope . He is perhaps best known for his book on the irrational number phi : The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number (2002).

**So What is the Golden Mean anyway?**

Represented as an equation, the golden ratio is this:

# a/b = (a+b)/a

The **Golden Ratio** translates to the irrational number 1.61803398875, known as the Greek letter, phi.

## Scientific Proof?

The premise that there is a mathematical basis for beauty is inherently difficult to prove.

Beauty is indeed as varied and subjective as human perception itself, yet if we look at varying aesthetic standards throughout history, we find certain recurring patterns behind what humans find beautiful.

The Golden Mean may be one of them. Perhaps Da Vinci was onto something after all.

At this point in time, there’s a great deal of information out there, and some of it from respected sources, to suggest that beauty may be reduced to a mathematical formula. I can’t say I am convinced, but I do believe that the idea is worthy of further

exploration.

While the so-called Golden Ratio may not define what we humans perceive as beautiful, it offers a useful, workable theory of what appeals to us, as well as how predictable that may be.

http://jwilson.coe.uga.edu/emat6680/parveen/ancient_egypt.htm

http://wwwhistory.mcs.stand.ac.uk/Biographies/Pythagoras.html

Originally published on https://paintedbrain.org/editorial/decoding-the-math-behind-beauty/

### Categories:

- Blog

## Follow