The golden ratio is often mentioned with regards to picture composition. But what is the golden ratio and what are its mathematical foundations? This tutorial contains everything you need to know about the golden ratio.

## What is the golden ratio?

The golden ratio is a compositional rule of thumb dating back to antiquity. It describes proportions that people find especially pleasing. The golden ratio is often found in nature and even in the human body, and is used to great effect in art, architecture, and even typography.

## The Mathematical Side of the Golden Ratio

The mathematics of the golden ratio are relatively simple. A line is divided into two parts “a” and “b” so that the ratio of the larger section (a) to the smaller section (b) is equal to the ratio of the whole length (a + b) to the larger section. This results in the formula: a / b = (a + b) / a. The outcome of this formula is an irrational number often called the “golden number” or phi in mathematics. The golden number phi is approximately equal to 1.618. Euclid was the first to provide a written description of the golden ratio in ca. 360-280 B.C.

## The Golden Ratio and the Fibonacci Sequence

In 1202, mathematician Leonardo Fibonacci described a series of rational numbers that result in the closest approximation of phi when adjacent terms are entered into the golden ratio formula. The Fibonacci sequence can be observed in nature, not exactly in rabbit population growth as he hypothesized, but in natural occurrences like leaf arrangements in plants. The Fibonacci sequence starts with the number 1 (or sometimes 0), and every number is the sum of the two preceding terms. So the first numbers would be 1, 1, 2, 1 + 2 = 3, 2 + 3 = 5, 8, 13 … and so on.

This series of numbers is directly related to the golden ratio. The larger the number in the sequence, the closer its proportions to the adjacent number will be to the golden number phi.

## The Golden Ratio in Photography

In photography, you can use the golden ratio as a helpful tool to create harmonious and pleasing compositions. Since the center of an image is often perceived as static or uninteresting, this division of space is often used in visual composition. The photograph is divided into nine rectangles along two horizontal and vertical lines according to the golden ratio. This is commonly known as a phi grid.

The image is then composed with important elements along the lines and at their intersections. For example, the horizon is along one of the vertical lines, while a person in the foreground is positioned along one of the vertical lines.

Tip: You can compose your image just off the phi grid to catch people’s attention – this breaks the harmony and builds additional tension. With this method, you can transform any fall photograph into a work of art!

## The Golden Ratio in Art

The golden ratio, also known as the divine proportion, can be found throughout art history dating back to ancient times. For example, the famous Venus de Milo sculpture of the goddess Aphrodite was made between 100 and 130 BC and contains golden proportions.

In the Renaissance, Leonardo da Vinci’s compositions also make masterful use of the divine proportion. His painting “The Last Supper” is constructed along golden proportions.

The world-famous Mona Lisa is also composed on a “golden triangle” – an isosceles triangle where the length of the sides and base create a golden ratio.

Try this composition for your portrait photos and experiment with the golden triangle. It creates an impressive composition that people view as balanced and harmonious. Our tip? Once you’ve nailed the composition, create an Acrylic Photo Print with top quality Kodak Pro Endura photo paper for luminous color and powerful contrasts.

Golden proportions are a common thread in works by the great masters, such as the Italian painter Raphael. His “Triumph of Galatea” consists of two sections. Not only does the forelock of Raphael’s Galatea separate the heavens from the earth, it also marks the piece’s golden sections. You can also find an invisible division in his “Sistine Madonna” – this time along the Madonna’s navel.

German artist Albrecht Durer’s self-portrait in a fur coat (from around the year 1500) shows the painter in a pose that had traditionally been reserved for Jesus or monarchs. Durer’s hair creates a triangle that divides the piece into golden sections. The painter’s face is also framed by vertical lines that structure the painting according to the golden ratio.

## The Golden Ratio in Faces and Bodies

With his “The Vitruvian Man”, Leonardo da Vinci created an impressive measuring system for the golden ratio based on the human body.

Today, plastic surgery is based on the golden ratio, since it is perceived as especially pleasing and beautiful. The more closely bodies and facial proportions are to the divine ratio, the more attractive the person is considered. According to studies by American plastic surgeon Stephen Marquardt, people find it ideal when the width of the nose multiplied by phi equals the width of the mouth.

## The Golden Ratio in Famous Architecture

Ancient temples were already built according to the golden ratio. The Great Pyramid of Giza (ca. 2590-2470 B.C.), for example, is perfectly proportioned by today’s standards. The Parthenon in Athens, which was built around 450 B.C., also closely approximates the proportions of the golden ratio.

St. Peter’s Basilica and the Cologne Cathedral were also created according to the divine proportion.

## Golden Ratios in Nature: The Nautilus’ Golden Spiral

If you split a rectangle according to the golden ratio, then split the smaller half the same way and so forth, eventually, you will have several nested quadrilaterals. Like the Fibonacci sequence, the side lengths will be equal to the sum of the length of the two rectangles it was divided into. If the corners are connected using a curved line, this creates a logarithmic spiral, also known as the golden spiral.

The shell of a nautilus grows in a similar spiral that does not change its curving shape even as it grows in size. This symmetrical spiral appears often in nature: in hurricanes, ferns, and even in entire galaxies.

Tip: Use the spiral for your own photographs to create a tension-filled composition. Show off the image in a large-format work of art by having it made into a photo canvas!

Whether it’s in the animal kingdom or the human body, the golden ratio is a fascinating phenomenon, the origins of which remains unknown. German physicist and philosopher Carl Friedrich von Weizsäcker summed the mystery up by saying: “Perhaps the ubiquitous, hidden mathematics of nature are the reason all beauty exists.”

Andrea Bruchwitz / Benjamin Arntz

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