The Golden Ratio – The Mathematical Secret of Beauty

The golden ratio basically describes a certain division ratio in geometry. This means that, for example, an item or other quantity is divided into two parts in a certain way. This classification has a mathematical background and has a very balanced and harmonious effect on us.

golden number

Specifically, the path of the golden ratio is divided into a shorter piece and a longer piece. It should be divided in such a way that the total distance divided by the longer distance results in the same longer distance divided by the shorter distance – which is an approximation of 1.618. This so-called golden number, which is referred to as “phi” in mathematics, is an irrational number. This means that it has an infinite number of decimal places and therefore cannot be fully computed and represented. But you can always get close to it.

This was achieved by the mathematician Leonardo Fibonacci, who in 1212 developed a numerical sequence in which the golden number could be approximated to more and more decimal places for the first time. In the Fibonacci sequence, which was later named after him, two consecutive numbers are always added. These two numbers result in the following number, which is added back to the one before it: 1,1,2,3,5,8,13 … 55, 89, 144 and so on. Dividing consecutive numbers into a mixture, you get closer and closer to the golden number. So 13 over 8 equals 1.625, and 144 over 89 equals 1.618. The more numbers in the sequence, the more accurately you calculate the golden number 1.61803398 …

A classic example of the golden ratio in architecture is the Parthenon in Athens

Ministry of Joy, Getty Images

golden beginnings

However, the mathematical principle behind the golden section was discovered long before that by the mathematician Euclid in antiquity. Around 300 BC, he dealt a lot with geometry and used compasses and rulers to construct a line with the exact division of the golden ratio. He also described it for the first time in his compositions “The Elements” and described the procedure as “division of the line according to the outer and middle ratio.”

However, the concept of the golden section was only formulated later, in the nineteenth century, by German mathematician Martin Ohm and developed from the “divine proportion”, as the ratio was called since the beginning of the sixteenth century. However, the golden ratio may have been used long before the beginning of mathematics and knowledge of numbers. Many stone age hand axes, tools of our ancestors tens of thousands of years old, were already made at that time according to proportions approximately corresponding to the golden section.

Beauty in art and architecture

The special relationship of the golden ratio has persisted throughout the history of art and architecture since the early days of human culture. Probably because most people automatically find this golden division ratio to be very harmonious. Relationships and proportions are beautifully and aesthetically created for the human eye. Many paintings, statues, and buildings are based on the “golden proportions”.

Among the world-famous examples are the “Mona Lisa” by the painter and mathematician Leonardo da Vinci or the statue “Venus von Milo”, whose proportion is based on the ratio of the golden division. But this relationship can also be found in other well-known paintings. For example, the “Last Supper”, a painting by da Vinci, can be divided into larger and smaller parts based on the figures shown, using the golden ratio, just as in Michelangelo’s fresco, The Creation of Adam, where the volumes of the figures are in relation to the golden ratio to each other.

What we don’t know today is to what extent artists actually paid attention to the golden ratio at the time or whether they unconsciously used it themselves through a natural sense of harmony of proportions. But what has been proven is that some people had this feeling as early as the Ice Age. Findings dating back about 15,000 years show carved figures in stone whose proportions correspond to the golden section.

However, the golden ratio can also be found in architecture. Famous examples are buildings such as the ancient Pantheon in Greece or the pyramid of Khufu in Egypt, where the golden section can be found in its dimensions. Notre Dame, Cologne Cathedral, Leipzig City Hall and many other buildings were also built according to this ratio.

Vitruvian man Leonardo da Vinci

The most well-known figure associated with the concept of the golden ratio is probably Leonardo’s “Vitruvian Man”.

The golden ratio even in our bodies

However, the golden ratio is by no means an “invention” of man. Originally it comes from nature, and amazingly, it is found everywhere in the world around us, even within ourselves. The height of our navel roughly divides our bodies by this ratio, and the ratio of the width of the nose to the mouth is also “golden”.

A well-known example of the golden ratio in our genealogy is the so-called “Vitruvian Man” by da Vinci, who fits into a square or circle with his arms and legs straight. Here the divine proportions can be found everywhere, both in the person depicted and in the relationship between the circle and the square.

… as well as in nature

The golden ratio can also be found in various forms in the animal and plant kingdoms. For example, the petals of roses and other plants grow in the golden corner. This means that two consecutive cards are at the same angle when you divide the circumference of the circle in the golden ratio. However, for plants, this is not an aesthetic issue, but rather helps them absorb as much sunlight and water as possible.

The so-called golden spiral can also be found. To represent this, the rectangle is divided according to the golden ratio, resulting in a new rectangle and a square. If you repeat this several times, several overlapping squares will be created, the side length of which is the sum of the side lengths of the next two smaller squares. So its size depends on the Fibonacci sequence. If you now connect the corners of the squares with a curved line, a golden spiral or a Fibonacci spiral will be created. This can be seen, for example, in the form of shells, ferns, hurricanes, and even pineapples and many other natural examples.

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