The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.
Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.
"Truchet from Truchet Tiles," by Robert Bosch (Oberlin College, Oberlin, OH)
18" x 18", Digital print on canvas, 2012
Father Sébastien Truchet (1657-1729) was a Carmelite clergyman. He was King Louis XIV's favorite hydraulic engineer. He designed fonts. And in 1704 he published an article, "Mémoire sur les combinaisons," that described his mathematical and artistic investigations into how a simple set of square tiles, each divided by a diagonal into a white half and a black half, can be arranged to form an infinity of pleasing patterns. Today, Truchet's tiles are known as, well, Truchet tiles. To create a Truchet-tile portrait of Truchet, I started with the orientations specified by Pattern D of Plate 1 of Truchet's article. I then allowed the diagonals of the tiles to "flex" or bend at their midpoints. To make a tile darker, I would flex the diagonal into the black half. To make a tile brighter, I would flex the diagonal into the white half. With my Flexible Truchet Tiles, I can approximate any grayscale image, using the image to "warp" any initial pattern of Truchet tiles. -- Robert Bosch