Beginning with the "golden section" and the development of the perspective representation of space in antiquity and the Renaissance, artists took geometric laws into account in order to set proportions in uniform relationships. Geometry at the same time opened up to them the possibility of giving their works a new dimension of spatial depth.

When modern art turned away from the task of mimetically imitating objects of the external world and instead set itself the task of depicting their essence in sensory experience, geometry retained its importance.

At the beginning of the 20th century, Cubism dissolved the conventions of form and space. The creative means of structuring the two dimensions of the canvas were deliberately reduced to highly simplified geometric forms such as nested planes, grid structures or lines of varying thickness.

Piet Mondrian (1872-1944) developed his own abstract geometric language from 1915 with his "Compositions". Black lines divide his works into areas, which are only weighted differently by the use of the primary colors yellow, red and blue. Theo van Doesburg (1883-1931) and the members of the de Stijl group assumed that geometry was a kind of universal language underlying every experience and every object. All sensory experience could thus find its counterpart in purely geometric forms.

The Russian avant-garde artist Kazimir Malevich (1878-1935) reduced his works such as "Black Square" or "Black Cross" to elementary geometric forms in order to be able to show the absolute of a "fourth dimension".

British artist Peter McClure expresses his fascination with geometry as the ordering force of the universe in works such as "Overlay"(1982) and "Linkage"(2008). Contemporary, digitized art based on geometric principles is created by Russian artist Alex Caminker.