MATHEMATICS AND ART

by Nikhat Parveen, UGA

The Golden Rectangle is considered to be one of the most pleasing and beautiful shapes to look at, which is why many artists have used it in their work.

The two artists, who are perhaps the most famous for their use of the golden ratio, are Leonardo Da Vinci and Piet Mondrian.

It can be found in art and architecture of ancient Greece and Rome, in works of the Renaissance period, through to modern art of the 20th Century. The Golden Rectangles present in the following Figures,  are quite obvious. However, various features of the Mona Lisa have Golden proportions, too.

The Parthenon was perhaps the best example of a mathematical approach to art.

Fig.1 Parthenon, Greece

Further classic subdivisions of the rectangle align perfectly with major architectural features of the structure.

Fig.2

Art Master Piece: Mona Lisa

Mona Lisa, is one of the most famous paintings in the world, and is a very good example of Da Vinci's use of the golden ratio in art.

If you draw a rectangle around Mona Lisa's face, that rectangle will turn out to be golden. The dimensions of the painting itself also form a golden rectangle. As well, the proportions of Mona Lisa's body exhibit several golden ratios. For example, a golden rectangle can be drawn from her neck to just above the hands.

Fig.3 Mona Lisa

According to one art expert, Seurat "attacked every canvas by the golden section". His Bathers has obvious golden subdivisions.

Fig.4 Bathers

Piet Mondarian

Piet Mondrian is a modern Dutch artist, who lived in 1872 - 1944. Although at the beginning of his career, Mondrian painted many landscapes, he later on moved to an abstract style in his work. Mondrian is famous for using horizontal and vertical black lines as the basis for a lot of his paintings. Like Da Vinci, Mondrian believed that mathematics and art were closely connected. He used the simplest geometrical shapes and primary colours (blue, red, yellow) to express reality, nature and logic from a different point of view. (Mondrian's point of view lies in the fact that any shape is possible to create with basic geometric shapes as well as any colour can be created with different combinations of red, blue, and yellow) The Golden Rectangle is one of the basic shapes, which keeps appearing in Mondrian's art:

Mondrian painted the following compositions in Red, Yellow and blue in 1942 and in 1926. There are many golden rectangles in this work.

Fig.5 Mondarian (1942)                            Fig.6 Mondarian (1926)

The more recent search for a grammar of art inevitably led to the use of the golden section in abstract art. La Parade, painted in the characteristic multi-dotted style of the French neo-impressionist Seurat (1859-1891), contains numerous examples of golden proportions.

Leonardo da Vinci (1451-1519). Leonardo had for a long time displayed an ardent interest in the mathematics of art and nature. He had earlier, like Pythagoras, made a close study of the human figure and had shown how all its different parts were related by the golden section.

Fig.8 Study of Human Proportions         Fig.9 Study of Facial Proportions

According to Vitruvious