Geometry in decorative arts. Egyptian patterns, such as the above, are still popular and influential in design today. Past and present, repeating designs have decorated fabrics, tiling, tapestries, rugs, wallpaper, etc.

Stephan Lochner: Madonna in the Rose Garden (c. 1430-1435). Much of pre-Renaissance art makes no attempt to portray three-dimensional space realistically. The figures represented are in a plane, and as a whole there is a geometric balance with use of repeating decorative patterns.

Albrecht Durer: Demonstration of Perspective Drawing of a Lute (1525). Albrecht Durer, an outstanding artist of the Renaissance in northern Europe, was an early promoter of geometric perspective and projective geometry, which he learned during trips to Italy. He wrote a treatise on the application of geometry to art, from which the above woodcut is taken

Bernardo Bellotto painting above shows the use of Renaissance ideas of geometric perspective in a later period for the purpose of realistic depiction of three-dimensional space.

Salvador Dali: Corpus Hypercubicus (1955). Spanish artist Salvador Dali goes beyond three-dimensionsl reality by using a four-dimensional cube (a hypercube) unfolded in three-dimensions as the cross, to portray Christ transcending the ordinary physical world, just as the hypercube transcends ordinary three-dimensional space.

Pablo Picasso: Girl Before a Mirror (1932). By the 20th century, artists had largely lost interest in photographic realism. Pablo Picasso played with perspective, showing multiple views of images dissected into raw geometric pieces.

Paul Klee: Family Prominade (1930). Paul Klee was well acquainted with mathematics and used geometry as the simple building blocks of his work. The arrangement and overlapping of simple shapes are used to suggest family relationships.

Paul Klee: Head of Man Going Senile (1922).

As art has become less representational and more conceptural, mathematics has appeared in artistic works more as the primary subject matter. Dutch artist Maurits Escher was introduced to non-Euclidean geometry by the mathematician H.M.S. Coxeter. Escher's angel and devil design is shown here in hyperbolic geometry.

Curtis D. Bennett. This representation of Escher's Circle Limit IV, uses computer programing to assign colors to demonstrate the Banach-Tarski Paradox of mathematics.

Art and Science in Chaos: Contesting Readings of Scientific Visualizations

Richard Wright

Digital Imaging Group

London Guildhall University