Math, Art, and Origami at MIT / Article in http://www.popsci.com

A father-and-son team study the science -- and art -- of folding

By Emily Stone Posted 04.27.2009
In the computer science lab where they work at MIT, Erik and Martin Demaine have a three-foot-tall metal and plastic sculpture that resembles a sleek, modernist version of a child's Tinkertoy creation.

Erik, a math prodigy who was honored in Popular Science's second annual Brilliant 10, and his father Martin, an artist who was drawn into math through his son, built the piece by starting with a three-dimensional hexagon they folded from paper. They then inputted the shape into a computer and virtually erased all of the paper, so that only the creases remained. Next, they turned back to the tangible and created a dynamic piece of art, using aluminum rods, locked together at the joints with plastic spheres, to represent each crease.

"We took something real and virtualized it, and then made it real again," explains Martin, 66, an MIT instructor and artist in residence.

They also took art, turned it into math and then back into art again. This belief that math and art are complementary endeavors is the key to the Demaines' work. The men use complex mathematics to create beautiful art, some of which is on display at the Museum of Modern Art in New York City. And they construct sculptures to help solve seemingly intractable math problems. Along the way, the lively and often goofy duo have inspired students to think more creatively about their discipline, and have shown the public that math doesn't have to feel inaccessible.

"We view them as very similar things," says Erik, a 28-year-old assistant professor, referring to math and art. "They're both creative processes. They're both about having the right idea."

Source:

http://www.popsci.com/scitech/article/2009-04/math-art-and-origami-mit

Modern Art and Mathematics

Many artists find, use and or abuse mathematics in their escapades. The results are always curious and intriguing.
Most people are familiar with the mathematics of the Renaissance artists, such as the use of the Golden Ratio. For example, Leonardo da Vinci used a complex formula based on the relationship 12:6:4:3. These ratios are also very present in music. 3:4 is the interval of one fourth, and 4:6 is a fifth etc. He thought making use of this ratio would “offer praise to the harmonies of the universe".

Naum Gabo Linear Construction No. 2 1970-71 Plastic and nylon filament (Sa) object 1149 x 835 x 835 mm

Modern Art is also prolific in the use the mathematics.Two very different artistic movements, the surrealists and the constructivists, discovered mathematical models at approximately the same time. Constructivist Naum Gabo began to draw direct inspiration from the forms of mathematical models in the early 1930’s. Surrealist photographer and painter Man Ray did a series of photographs in 1936 of mathematical models housed at the Poincaré Institute in Paris.


Henry Moore Stringed Figure, 1937
cherry wood and string on oak base

Henry Moore (1893-1986) used string in many of his sculptures for a short period of time, and this was influenced by stringed models that he had seen at the Science Museum in London. As Moore himself says: Undoubtedly the source of my stringed figures was the Science Museum...I was fascinated by the mathematical models I saw there, which had been made to illustrate the difference of the form that is halfway between a square and a circle. One model had a square at one end with twenty holes along each side, making eighty holes in all. Through these holes strings were threaded and lead to a circle with the same number of holes at the other end. A plane interposed through the middle shows the form that is halfway between a square and a circle. One end could be twisted to produce forms that would be terribly difficult to draw on a flat surface. It wasn't the scientific study of these models but the ability to look through the strings as with a bird cage and see one form within the other which excited me. [Moore, p. 105]

Barbara Hepworth (1903-1975) is also known for the use of string in her sculpture, and upon viewing some of her pieces, one is reminded of certain mathematical models. Hepworth was an abstract sculptor, and had some involvement with the Constructivist movement, particularly from the mid 1930's to the mid 1940's, when Naum Gabo was living nearby. The effect of mathematical models on Hepworth is less clear than it was on Henry Moore. It is clear, however, that Hepworth knew about mathematical models.

Barabara Hepworth also had a close and productive relationship with J.D. Bernal, a crystallographer who was interested in the relationship between art and science. Apparently, Hepworth enjoyed visits from Bernal, during which he would discuss with her the mathematics and geometry in her works [Barlow]. Hepworth had an interest in "higher geometry" and she probably viewed the models at the school in Oxford herself, but the exact influence of the models in unclear.