Mathematics plays a key role in determining proportion, symmetry, shape and patterns, and is therefore an integral part of visual art. Mathematics can be used to explain and describe works of art and architecture.
One of the important concepts throughout art history has been that of the so-called golden rectangle or golden ratio, a set of proportions that has been found to be aesthetically pleasing and can be found on the human body itself. The golden ratio is 1:0.618, and essentially divides a composition into 1/3 and 2/3. The golden ratio was used extensively by classical architects in creating well-known buildings, such as the Parthenon in Athens, Greece. It was also used by painters such as Leonardo da Vinci, Seurat and Piet Mondarian in both figurative and abstract compositions.
The use of lines and the creation of planes or three dimensions in a two-dimensional painting can be achieved through the use of mathematical principles. Artist M.C. Escher created and manipulated the illusion of planes and structures that were actually mathematically impossible, but which appeared plausible.
Many of the canons of traditional art are based on mathematical principles, such as the creation of perspective and patterning, which creates ornamental effects.