math of beauty

Beauty is cherished by all of us, as it evokes perfection. The essence of beauty consists of spiritual and emotional qualities rather than physical ones. These features affect many areas of our lives. Although not the most important aspect of our lives, beauty has an important power to attract attention, to arouse respect and admiration in the eyes of the beholders. Because beauty is a concept based on centuries ago, constantly changing and developing, and we are all affected by it.

Although beauty is an immeasurable concept, harmony associated with beauty can be explained by formulas.

What is the harmony of face proportions?

Studies show that when the facial proportions are not balanced, attention is focused on the area of ​​disproportion.

This is caused by dark or uneven teeth, gaps, smiles where the gums look too much (gummy smile) and disproportionate structures on the face (for example, the ratio of the lips, nose, and eyes alone, to each other, and to other areas of the face). The concept of beauty is often about harmony and harmonious proportions. The term ‘ratio’ is the mathematical side of beauty.

Golden Ratio: 1.618

The Golden Ratio is a product of the natural principle of the laws of equilibrium, not of mathematical imagination. In short, we can call the golden ratio “the ratio of the eye system”.

Being aware of this, artists have used this feature wisely throughout history and created works that look beautiful to the eye. For example, the ratio of the height to the width of the Mona Lisa painting gives the golden ratio. When you draw a rectangle around the head of the Mona Lisa, the four edges are a golden rectangle. When you divide this rectangle with a line that you will draw at eye level, you will again get a golden ratio. The dimensions of the picture also form the golden ratio.

B.C. Pythagoras (Pythagoras), one of the greatest mathematicians of all time who lived in the 500s, expressed the following thoughts about the golden ratio:

“The ratio of a person’s whole body to the navel, the ratio of the long and short sides of a pentagram, the ratio of the long and short sides of a rectangle are all the same. Why is that? Because the ratio of the whole piece to the big piece is equal to the ratio of the big piece to the small piece.”

What do the pyramids in Egypt, Leonardo da Vinci’s Mona Lisa, sunflowers, snails, pinecones and your fingers have in common? Golden Ratio?

The answer to this question is hidden in a series of numbers found by the Italian mathematician Fibonacci. The characteristic of these numbers, also called Fibonacci numbers, is that each of the numbers in the sequence consists of the sum of the two preceding numbers.


233 / 144 = 1.618
377 / 233 = 1.618
610 / 377 = 1.618
987 / 610 = 1.618
1597 / 987 = 1.618
2584 / 1597 = 1.618

Artists, scientists and designers take the human body, whose proportions are determined according to the golden ratio, as a measurement while doing their research or presenting their products. While making their designs, Leonardo da Vinci and Corbusier took the human body as a measurement according to the golden ratio. Neufert, one of the most important reference books of today’s architects, is also based on the human body determined according to the golden ratio.

The Golden Ratio in the Human Body

The first example that can be given to the golden ratio in the human body is that when the distance between the navel and the foot is accepted as 1 unit, the human height corresponds to 1.618. Apart from this, some other golden ratios in our body are as follows:

Between fingertip and elbow / Between wrist and elbow,
Distance from shoulder to head / Head length,
Distance from navel to head end / Distance from shoulder level to head end,
Between the navel-knee / Between the knee-toe.

The human face also has many golden ratios. But don’t try to take a ruler and measure people’s faces right away. Because this ratio is valid for an ‘ideal human face’ accepted by scientists and artists. Not every face can be expected to comply with this ratio. This ratio can only be found on ideal faces.

For example, the ratio of the sum of the widths of the two front teeth in the upper jaw to their height gives the golden ratio. The ratio of the width of the first tooth from the center to the second tooth is also based on the golden ratio. These are the ratios that a dentist can take into account when creating an aesthetic and ideal smile. Aesthetic dentistry settles on a more scientific platform with the calculation and application of these golden ratios. Apart from these, some other golden ratios on the human face are as follows:

Length of the face / Width of the face,
Between the lips and eyebrows / Nose length,
Length of the face / Between the chin tip and the junction of the eyebrows,
Mouth length / Nose width,
Nose width / Between nostrils,
Interpupillary / Between the eyebrows.