MATHINFINITY

MATHEMATICS AND FINE ARTS

Art means creating "beauty" in the environment, image, objects, movements, sound and so on based combined human factors such as techniques, wish, imagination and experience. This kind of beauty can be shared or exchanged, and it can arouse collective emotions as well as individual thinking. In the huge world of Art, painting, sculpture, architecture, literature, music, drama, dance, movie, photography and the like belong to the field of Fine Art.

Human's sense of aesthetics is not affected by their language or cultural background. Aesthetic lovers usually have interest in fine art. A lot of great masterpieces of art have included the application of arithmetic, algebra, plane geometry, solid geometry, analytic geometry, topology, perspective and symmetry. Although human and animal forms are prohibited in art pieces according to the Muslim creeds, many Muslim artists have made used of mathematics to create numerous geometric and mosaic designs as seen in their carpets and floor tiles.

Golden Ratio and Fine Arts

Compliments are given to the human body due to the appropriate proportion of the head and the limbs, as well as the balance of the entire body. Among the famous sculptures of ancient Greece, Venus de Milo, Athena and Apollo all have their legs extended so that the proportion of the length from the belly button to the bottom of the feet and the height of the person meets the Golden Ratio (0.618). The Golden Ratio also appears in a lot of famous paintings, sculptures and even photographs, such as Mona Lisa by Leonardo da Vinci, The Gleaners by Jean-François Millet, The Great Wave off Kanagawa by Katsushika Hokusai, Hyères,France by Henri Cartier-Bresson, etc.

Geometric Figures and Fine Arts

Point, line, plane and other geometric figures are essential elements for studying mathematics. Point is also used in painting like Pointillism. Instead of mixing the colors well and painting them on the canvas, the painter directly makes dots onto the canvas with colors like red, yellow and blue to let different colors blend together naturally to create unique patterns. One important masterpieces of this kind is A Sunday Afternoon on the Island of La Grande Jatte by Georges-Pierre Seurat. On the other hand, many painters also study mathematics in order to merge it with art. Leonardo da Vinci successfully applied geometric perspective in painting The Last Supper by creating a 3-dimensional space on a flat wall. Maurits Cornelis Escher had used hyperbolas in his wood carving Circle Limit II to express his enthusiasm in geometry.

Interactive Game

Try to place the plastic sheets onto their corresponding positions as shown in the figure and discover the relationship between mathematics and masterpieces of art in terms of their layout and structure.

Did you know?

1) On the top right-hand corner of the masterpiece, Melancholia, by the German artist, Albrecht Durer, a magic square of order four was painted. What is more interesting is that the numbers of the year 1514 also appear in the magic square.

2) Cubism as created by Pablo Picasso and Georges Braque emphasizes on breaking up and reassembly. The unique Collage technique was developed from it thereafter.