Concrete Art – The Significance of Mathematics, Geometry and Proportions for Aesthetics and Artistic Creation

There are many sources of inspiration for art. Beauty, anger, grief, and religion are responsible for an endless wealth of works in cultural history.

appears somewhat more austere geometric art , as it—to use the term "Art concret "—does not aim to depict anything real or tangible, but rather locates its entire source in mathematics and scientific thought. However, this approach not only creates unique, exciting, and easily accessible works, but is also surprisingly widespread in art history.

Concrete Art – basic ideas, important artists and history

The concept of Concrete Art is far less complex than many assume. It is neither Constructivist nor Abstract. While the latter abstracts real-world phenomena, Concrete Art creates something tangible from something conceptual.

It is a geometric art form that does not present the audience with the enigma of any symbolism, but is derived from something comprehensible and provable.

Precisely because it doesn't imitate feelings, it is a sensually perceptible art. The observer can concentrate fully on the interplay of forms and colors . Instead of translating something experienced onto a material, they can engage with the material itself. This art directly produces aesthetic suggestions and their corresponding systems of order.

Concrete art has numerous predecessors and forerunners, not only in art itself, but also in mathematics and the natural sciences. It is closely related, for example, to the Bauhaus or Cubism. Since the turn of the century, artists have increasingly distanced themselves from the representation of the visible world.

However, the formal starting point of the movement is often placed with Kazimir Malevich's painting "Black Square" from 1915. This work broke decisively with the prevailing art tradition up to that point.

in the Netherlands explored De Stijl movement similar aesthetic concepts. This group of painters, architects, designers, and publishers, including artists such as Theo van Doesburg, Georges Vantongerloo , and Piet Mondrian , embraced an ascetic style and functionality.

It was Theo van Doesburg who gave Concrete Art its name in 1924. The guidelines of the new movement were then formalized with the founding of the Art Concret group, which in 1930 encompassed a broad style of non-representational, geometric art .

The group explicitly positioned itself against the realistic modes of representation and the fascination with the inexplicable characteristic of Dadaism. They also sought to counter the anti-rational stance of Surrealism . Although Art Concret soon dissolved, its ideas have endured to this day, not only in art but also in related fields such as architecture and design.

Can offices and traffic signs be considered concrete art?

Dr. Simone Schimpf is the director of the Museum of Concrete Art in Ingolstadt and chairwoman of the Foundation for Concrete Art and Design.

Pythagoras and his influence on aesthetics and art

, Pythagoras of Samos remains an enigmatic figure for scholars. Praised by some as a pioneer of Greek natural science, mathematics, and philosophy, others see him primarily as an activist in the name of religion. His influence on artistic aesthetics, however, is largely undisputed.

Here, too, the historical dual role of Pythagoras of Samos becomes clear. Ideas of holistic harmony and the psychology of the soul are intertwined with mathematical derivations.

In late antiquity and the Middle Ages, it was widely believed that Pythagoras was the founder of mathematics. He was especially credited as the discoverer of the Pythagorean theorem. This theorem states that in a right-angled triangle, the cube of the longest side is equal to the sum of the cubes of the shorter sides.

How Leonardo da Vinci proved the Pythagorean theorem

What is special about Leonardo da Vinci's proof of the Pythagorean theorem is that he presents it an optical-logical approach . It works as follows:

If you imagine a right-angled triangle with vertices A, B, and C, and assume the right angle is at C, you can visually picture the two squares of the shorter sides (legs) whose diagonals form a line g through point C. The original triangle is then reflected across line g. Both triangles together with the squares now form a hexagon.

Now the original triangle is duplicated again and attached to the opposite side of the imaginary square on the hypotenuse. Here too, the square on the hypotenuse, together with the two triangles, forms a hexagon. If this hexagon is then rotated around the vertices A or B of the original triangle, it can be seen that both hexagons are congruent.

Since one hexagon consists of the square of the hypotenuse and two original triangles, and the other of the latter plus two squares of the legs, the four triangles can simply be disregarded (while maintaining the area ratio of the hexagons). This leads to the conclusion that the two squares of the legs must be the same size as the square of the hypotenuse.

Fibonacci, the Golden Ratio and other geometric concepts in art, photography and architecture

Concrete Art set out to “pure expression of harmonious measure and law,” find Max Bill formulated it. It is therefore not surprising that the mathematical principle of the Golden Ratio engaging with this principle is practically a defining aspect of their identity Jo Niemeyer .

Simply put, the Golden Ratio is a division ratio in which a whole is divided into two parts of different sizes, such that the larger part is in the same ratio to the smaller part as the whole is to the larger part.

Throughout history, individual artists and entire art movements have repeatedly found this ratio particularly appealing, harmonious, or otherwise interesting. There is no objective evidence for this. However, numerous examples of this proportion can be found in nature, for example in the arrangement of leaves and flowers or crystal forms.

The origin of this principle is unclear. However, references to it can be found, for example, in Greece at least since the 4th century BC. In Europe, the Golden Ratio is often associated with the so-called Fibonacci sequence . The Italian mathematician used it to describe the growth of a rabbit population. The rule of this sequence of natural numbers is that the last two numbers in the sequence are added together to form the next (1, 1, 2, 3, 5, 8...).

The physicist Johannes Kepler later pointed out that the ratios of consecutive Fibonacci numbers approach the Golden Ratio arbitrarily closely. Fibonacci's general connection to the Golden Ratio is remarkable. Like the principle of the Golden Ratio itself, the sequence of numbers was known long before his time – both in ancient Greece and in India. As a well-traveled scientist, he was likely aware of this and did not delve further into the connection himself.

It is assumed that the Golden Ratio used in art and architecture also Michelangelo's "The Creation of Adam," illustrate this mathematical ratio.

Mathematics and Science in Art

This is just a brief overview of the influence of mathematical and scientific principles on art and our aesthetic sensibilities in general. Forms, the combination of colors, material combinations – all of these can be traced back to scientific principles.

It is in the viewer's interest to continually re-establish these connections.