The tiles don’t seem like much at first glance: they can be one of two diamond shapes, either fat or skinny. Paul Stacy, an Australian landscape architect, got seduced by the beauty of math when a friend brought him some ceramic Penrose tiles. That aesthetic beauty was easy to see at the 2009 Joint Mathematics Meetings in Washington, D.C., January 5–8, which showcased mathematics research and also invited artists and mathematicians to come together to create a display of mathematical art. Friedman used the one in the middle as the basis for his sculpture. The usual, simplest configuration is on the left. Paul Stacy TREFOIL KNOTS These three knots are different configurations of an overhand knot, called a trefoil. Vladimir Bulatov SWARMING PENTAPLEX The center of this painting is a Penrose tiling. Nat Friedman RHOMBIC DODECAHEDRON I: Vladimir Bulatov took inspiration for this sculpture from an unusual polyhedron. Suman Vaze TREFOIL KNOT MINIMAL SURFACE This is the shape a soap film forms over the simplest knot there is, a trefoil. Vladimir Bulatov MONGE’S THEOREM Suman Vaze took inspiration from a theorem in geometry for this painting. A rhombic dodecahedron has the same symmetries as a cube, and this spot corresponds to the corner of a cube. THREE-FOLD SYMMETRY The arms of each “starfish” polyhedron connect at symmetry points. Artist Paul Stacy made the joints between the tiles invisible when he painted it. ![]() PENROSE TILES UNDERNEATH This shows the pattern of the Penrose tiles at the center of Stacy’s artwork. ![]() Mathematics is beautiful: intellectually elegant, exquisitely austere and pretty.
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