Geometric abstraction is a form of abstract art based on the use of geometric forms sometimes, though not always, placed in non-illusionistic space and combined into non-objective (non-representational) compositions. Although the genre was popularized by avant-garde artists in the early twentieth century, similar motifs have been used in art since ancient times.

Geometric abstraction has been called a chapter of abstract art developed since the 1920s, and is based on the use of simple geometric shapes combined in subjective compositions on unreal spaces. It arises as a reaction to the excessive subjectivity of the plastic artists of earlier times in an attempt to distance themselves from the purely emotional. The critical discourse of these artists is complemented by an exacerbated exaltation of the two dimensions in the face of the effort of most of the previous movements to try to represent a three-dimensional reality.

Wassily Kandinsky was its main precursor and the most influential teacher in a generation of abstract artists. Kasimir Malévich and Piet Mondrian are also among their drivers and in both of them you can also appreciate the influence of ancient cultures that used geometry as artistic and decorative expression. It is the case of the ceramics and mosaics that are conserved of the Islamic art, forced by the religious precept to avoid the representation of the human figure. Also the classical cultures of ancient Greece and imperial Rome, in which decorative elements were used profusely without recognizable references in reality.

The abstract expressionism, which are creators of representatives as Jackson Pollock, Franz Kline, Clyfford Still, and Wols, represents the exact opposite of geometric abstraction.

The principles of geometric abstractionism are:

Abolition of the third dimension;
Independence from emotional values, contrary to what Vasili Kandinskij says, painting must not express feelings;
The means of expression are the line and the color;
The ideal shape is the rectangle because in it the line is straight without the ambiguity of the curve;
Use of primary colors: yellow, blue, red.

History
Geometric abstraction is present among many cultures throughout history both as decorative motifs and as art pieces themselves. Islamic art, in its prohibition of depicting religious figures, is a prime example of this geometric pattern-based art, which existed centuries before the movement in Europe and in many ways influenced this Western school. Aligned with and often used in the architecture of Islamic civilations spanning the 7th century-20th century, geometric patterns were used to visually connect spirituality with science and art, both of which were key to Islamic thought of the time.

In 1917 the magazine De Stijl was born in the Netherlands and together with it the artistic movement of neoplasticism by various artists, including Piet Mondrian (1872 – 1944). Their abstractionism is of a geometric type based on the creation of pure and two-dimensional shapes.

The dividing line to abstract art is called geometric abstractionoutplayed by encompassing both artistic positions. This probably goes back to the influential, cosmopolitan group of artists Abstraction-Création, founded in France in 1931 by Georges Vantongerloo, among others, with many very prominent members. The name of the group describes the wide range of art movements represented in it. “Création” stands for the creation of a work of art out of nothing, more precisely without a material starting point: the position of the later concrete art. In order to bring together as many “progressive” artists as possible in this group, attempts were made to blur the existing dividing lines, but (until today) did not manage entirely without distinctive terms:Lyrical abstraction (French abstraction lyrique) and just geometric abstraction (abstraction géométrique).

In the North American Art since 1945 equal to look at several art movements (and its global offshoots) in the tradition of geometric abstraction, for example abstraction the post-painterly, the Hard Edge, the Color Field Painting and minimalism.

Scholarly analysis
Throughout 20th-century art historical discourse, critics and artists working within the reductive or pure strains of abstraction have often suggested that geometric abstraction represents the height of a non-objective art practice, which necessarily stresses or calls attention to the root plasticity and two-dimensionality of painting as an artistic medium. Thus, it has been suggested that geometric abstraction might function as a solution to problems concerning the need for modernist painting to reject the illusionistic practices of the past while addressing the inherently two dimensional nature of the picture plane as well as the canvas functioning as its support. Wassily Kandinsky, one of the forerunners of pure non-objective painting, was among the first modern artists to explore this geometric approach in his abstract work. Other examples of pioneer abstractionists such as Kasimir Malevich and Piet Mondrian have also embraced this approach towards abstract painting. Mondrian’s painting “Composition No. 10” (1939–1942) clearly defines his radical but classical approach to the construction of horizontal and vertical lines, as Mondrian wrote, “constructed with awareness, but not with calculation, led by high intuition, and brought to harmony and rhythm.”

Just as there are both two-dimensional and three-dimensional geometries, the abstract sculpture of the 20th century was of course no less affected than painting by geometricizing tendencies. Georges Vantongerloo and Max Bill, for example, are perhaps best known for their geometric sculpture, although both of them were also painters; and indeed, the ideals of geometric abstraction find nearly perfect expression in their titling (e.g., Vantongerloo’s “Construction in the Sphere”) and pronouncements (e.g., Bill’s statement that “I am of the opinion that it is possible to develop an art largely on the basis of mathematical thinking.”) Expressionist abstract painting, as practiced by artists such as Jackson Pollock, Franz Kline, Clyfford Still, and Wols, represents the opposite of geometric abstraction.

Relationship with music
Abstract art has also historically been likened to music in its ability to convey emotional or expressive feelings and ideas without reliance upon or reference to recognizable objective forms already existent in reality. Wassily Kandinsky has discussed this connection between music and painting, as well as how the practice of classical composition had influenced his work, at length in his seminal essay Concerning the Spiritual in Art.