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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 ...
Geometricae is an art magazine covering international geometric abstraction. It was founded in 2015 [ 1 ] as a non-profit digital magazin by a group of artists and art critics led by architect Gianfranco Spada, in Valencia , Spain.
An abstract structure is an abstraction that might be of the geometric spaces or a set structure, or a hypostatic abstraction that is defined by a set of mathematical theorems and laws, properties and relationships in a way that is logically if not always historically independent [1] of the structure of contingent experiences, for example, those involving physical objects.
Those abstract things are then said to be multiply instantiated, in the sense of picture 1, picture 2, etc., shown below. It is not sufficient, however, to define abstract ideas as those that can be instantiated and to define abstraction as the movement in the opposite direction to instantiation. Doing so would make the concepts "cat" and ...
Fig. 2: Homothety transforms a geometric figure into a similar one by scaling. In ancient Greek mathematics, "space" was a geometric abstraction of the three-dimensional reality observed in everyday life. About 300 BC, Euclid gave axioms for the properties of space. Euclid built all of mathematics on these geometric foundations, going so far as ...
The second geometric development of this period was the systematic study of projective geometry by Girard Desargues (1591–1661). [32] Projective geometry studies properties of shapes which are unchanged under projections and sections , especially as they relate to artistic perspective .
Al Held (October 12, 1928 – July 27, 2005) was an American Abstract expressionist painter.He was particularly well known for his large scale Hard-edge paintings. [1] As an artist, multiple stylistic changes occurred throughout his career, however, none of these occurred at the same time as any popular emerging style or acted against a particular art form. [2]
In the opposite direction of abstraction, we may apply a compatible field structure to the geometric plane, giving rise to the complex plane and the major area of complex analysis. The complex field has only two isomorphisms that leave the real line fixed, the identity and conjugation .