Mathematics: Muse, Maker, and Measure of the Arts (11w5070)

Mathematics and arts have a long historical relationship. Tile mosaics since the early civilizations combine both artistic beauty and mathematical complexity. The ancient Egyptians and ancient Greeks knew about the golden ratio, regarded as an aesthetically pleasing ratio, and incorporated it into the design of monuments including the Great Pyramid, the Parthenon, the Colosseum. There are many examples of artists who have been inspired by mathematics and studied mathematics as a means of complementing their works. The Greek sculptor Polykleitos prescribed a series of mathematical proportions for carving the ideal male nude. Renaissance painters developed the theory of perspective, and many, including Piero della Francesca, became accomplished mathematicians themselves. The interplay of mathematics and art has continued to flourish throughout our history. Mathematics had greatly inspired artists as M. C. Escher, Picasso, Salvador Dali and artistic movements such as the minimalist and abstract art. Conversely, the art of tiling had contributed to the discovery of Penrose tiles and the study of aperiodic structures such quasicrystals, one of the most important areas in mathematics. The study of geometry and advent of digital age have sown the seeds for a revolution in the arts. The processing power of modern computers allows mathematicians and non-mathematicians to visualize complex mathematical objects such as the Mandelbrot set and other fractal sets. The artistic beauty of such sets had attracted many mathematicians to discover fundamental properties they play in dynamical systems and chaos. In the modern industry of computer animation, fractals play a key role in modeling mountains, fire, trees and other natural objects. Fractals are an example of the growing field of generative art, which refers to ways to systematically and autonomously generating artwork in an algorithmic way using a computer. The workings of systems in generative art often rely on various fundamental scientific theories such as Complexity theory and Information theory. Generative art is not limited to abstract art. By combining it with Learning Theory it is even possible to artificially generate paintings and music that mimic known masters. While generative art refers to an autonomous system for generating artwork, artists today are increasingly relying on mathematics and computers to aide their creative work. Besides painting and music, the intricacy of origami highlights the fusion of mathematics and art. Modern computing has allowed us to make complex geometric designs that have led to the design and creation of origami figures whose complexity and delicacy cannot even be imagined in the past.