The Visual Mind II (Leonardo Book Series)
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Mathematical forms rendered visually can give aesthetic pleasure; certain works of art -- Max Bill's Moebius band sculpture, for example -- can seem to be mathematics made visible. This collection of essays by artists and mathematicians continues the discussion of the connections between art and mathematics begun in the widely read first volume of The Visual Mind in 1993.
Mathematicians throughout history have created shapes, forms, and relationships, and some of these can be expressed visually. Computer technology allows us to visualize mathematical forms and relationships in new detail using, among other techniques, 3D modeling and animation. The Visual Mind proposes to compare the visual ideas of artists and mathematicians -- not to collect abstract thoughts on a general theme, but to allow one point of view to encounter another. The contributors, who include art historian Linda Dalrymple Henderson and filmmaker Peter Greenaway, examine mathematics and aesthetics; geometry and art; mathematics and art; geometry, computer graphics, and art; and visualization and cinema. They discuss such topics as aesthetics for computers, the Guggenheim Museum in Bilbao, cubism and relativity in twentieth-century art, the aesthetic value of optimal geometry, and mathematics and cinema.
with Emil and Alfred Roth, I was building the Doldertal houses which in those days were Visual Mathematics: Mathematics and Art 77 much talked about. One day, Marcel told me he had been commissioned to design a house for an exhibition in London. It was to be the model of a house in which everything, even the fireplace, would be electric. It was obvious to all of us that an electric fireplace, which glowed without flames, would not be a particularly attractive object. Marcel asked me if I would
wood lamination, I consecutively produced a series of geometries, each within the enclosure of the preceding. First was a helical column—in cross section a circle six inches in diameter—that spirals clockwise around the longitudinal axis of the original lamination: this linear axis was simply a planar equilateral triangle with rounded vertices. Continuing to subtract, I next created a twisting band—in cross section a three-by-six-inch rectangle with rounded corners—within the previous helical
historical period and the context, one finds substantial agreement among mathematicians as to which mathematics is to be regarded as beautiful. This agreement is not merely the perception of an aesthetic quality superimposed on the content of a piece of mathematics. A piece of mathematics that is agreed to be beautiful is more likely to be included in school curricula; the discoverer of a beautiful theorem is rewarded by promotions and awards; a beautiful argument will be imitated. In other
will go to any length to deny the logical role of any such concept. Mathematical beauty is the expression mathematicians have Gian-Carlo Rota 12 invented in order to admit obliquely the phenomenon of enlightenment while avoiding acknowledgment of the fuzziness of this phenomenon. They say that a theorem is beautiful when they mean to say that the theorem is enlightening. We acknowledge a theorem’s beauty when we see how the theorem “fits” in is place, how is sheds light around itself, like
Editor’s note: Gian-Carlo Rota was born on 27 April 1932, to a prominent family in Vigevano, Italy. He died at the age of 66 on 19 April 1999. Dr. Rota The Phenomenology of Mathematical Beauty 13 was the only MIT faculty member ever to hold the title of professor of applied mathematics and philosophy. His uncle by marriage, Ennio Flaiano, wrote scripts for Federico Fellini’s films, including La Dolce Vita. The wife of Flaiano, Rosetta, was a mathematician at the University of Rome. Flaiano was