Mathematical Beauty - Mathematics and Art

Mathematics and Art

The psychology of the aesthetics of mathematics is studied post-psychoanalytically in psychosynthesis (the work of Piero Ferrucci), in cognitive psychology (illusion studies using self-similarity in Shepard tones), and the neuropsychology of aesthetic appreciation. Examples of the use of mathematics in the arts include:

• Music – the Stochastic music of Iannis Xenakis, counterpoint of Johann Sebastian Bach, polyrhythmic structures (as in Igor Stravinsky's The Rite of Spring), the Metric modulation of Elliott Carter, permutation theory in serialism beginning with Arnold Schoenberg, and application of Shepard tones in Karlheinz Stockhausens Hymnen.
• Choreography – shuffling has been applied to choreography as in the Temple of Rudra opera.
• Visual arts – examples include applications of chaos theory and fractal geometry to computer-generated art, symmetry studies of Leonardo da Vinci, projective geometries in development of the perspective theory of Renaissance art, grids in Op art, optical geometry in the camera obscura of Giambattista della Porta, and multiple perspective in analytic cubism and futurism.

The symmetries of two dimensional tessellations and three dimensional mathematical objects can evoke feelings of "mathematical beauty" as expressed by Bertrand Russell. This may apply to polyhedrons (three dimensional geometric solids), many of which show perfect symmetries that, combined with the use of colours, result in a visual experience that many consider attractive. The use in art of such objects or tessellations is limited though, as this beauty is often considered soulless and does not evoke feelings of emotion. The Dutch graphic designer M.C. Escher created mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, visual paradoxes and tessellations. Computer generated art is based on mathematical algorithms.