## The Mathematics Of Beauty

In all art and design we often recant the timeless adage – ‘When it comes to matters of opinion debate is futile. There is no accounting for taste’. Yet we can also objectively say that there are bad tattoos and bad drawings. If one takes away the personal preference of art and design to simply concentrate on the composition or foundation of a piece – can there be common denominators? An objective tool for the measurement of success or failure in art?

These more generalized philosophical questions will be explored in later sections. Here we briefly look into the more classical mathematical measurements of beauty:

#### The Traditional Measurements

A growing body of scientific studies based on an ancient mathematical ratio suggests that physical attractiveness could be real and quantifiable rather than purely subjective. Greek and Egyptian mathematicians believed in a theory of beauty and maths. They believed that a common element existed in all things humans found attractive.

This element, known as the ‘golden ratio’ or ‘divine proportion’ is a mathematical ratio of 1:1618 – with the number 1.618 being known as ‘phi’. The golden ratio is based on the Fibonacci sequence, in which the first two numbers are 1 and each subsequent number equal to the sum of the previous two numbers. This sequence goes 1, 1, 2, 3, 5, 8, 13, 21 and so on. The average ratio of each consecutive pair of numbers (1/1, 2/1, etc.) becomes closer and closer to 1:1.618

This ratio recurs frequently in nature. It can be observed in the spiral of a seashell or in the distribution of petals on a sunflower. The ratio of the lengths of the thorax and abdomen in most bees is close to the golden ratio and is occurs in sever man-made creations considered particularly beautiful – from Mozart’s music to buildings such as the Parthenon.

As early as the 15’th century the Italian architect Leon Battista Alberti believed that beauty was matter of proportion and that if a body was divided into 600 parts, beauty would be a “harmony of all the parts, in whatsoever subject it appears, fitted together with such proportion and connection, that nothing could be added, diminished or altered, but for worse”. The proportion which he believed would secure a harmony of all the parts was phi.

The Italian Renaissance polymath Lenoardo Da Vinci was also fascinated by this relationship. One of his most famous works, the drawing of the Vitruvian Man, showed how the human body conforms to the golden ratio. If you mesaure from the soles of your feet to your navel and from the soles of your feet to your head, in most people the longer the distance is 1.618 times the shorter one. The same relationship occurs if you measure from your fingertips to your elbow and from your fingertips to your shoulder. The face of Da Vinci’s Mona Lisa is also structured around this ratio.

It was only in the 20th century, with the advent of cosmetic surgery, that man was able to capitalize on this knowledge and use it to help improve our looks. It is now thought that this ratio could hold the key to the modern ideal of the ‘perfect’ face and body.

Stephen Marquardt, a retired Californian plastic surgeon who also researches attractiveness, has designed a mask using phi. This mask applies the golden ratio to the human face. For example, the ideal ratio between the width of the nose and the width of the mouth is 1:1.618 – so the closer a face fits the mask, he finds, the more attractive the face is perceived to be. To prove his case he applied the proportions of the mask to the faces of actors and timeless beauties such as Marilyn Monroe, Marlene Dietrich, Pierce Brosnan, Tom Cruise and Egyptian queen Nefertiti. The mask was a perfect fit on all but Tom Cruise.