Equivalent is a three-piece, 3D-printed sculpture comprised of three topologically equivalent variations of the Borromean rings. In the Borromean rings, no two of the three rings are linked, so if any one of them is destroyed, the remaining two rings will come apart. There are male rings, female rings, and plain rings, which symbolize the bond of marriage. For the photograph, we positioned Equivalent on a piece of Lenox china (a wedding gift).
Copies can be ordered at Shapeways.
Embrace is a two-piece water-jet-cut sculpture of a two-component link (two interlaced curvy triangles). The inside piece is quarter-inch-thick stainless steel, and the outside piece is quarter-inch-thick brass. The gap between the two pieces is the solution to a 726-city instance of the Traveling Salesman Problem. The gap is both the salesman's tour and the path along which the water-jet-cutter cut through the metal disks.
Embrace was awarded First Prize at the 2010 JMM Mathematical Art Exhibition in San Francisco.
Karma Ball is a hand-carved three-inch-diameter ball of maple. The channel is deep enough and wide enough to hold a half-inch-diameter ball of steel. It is possible to pick up the ball of wood and maneuver it so that the ball of steel will roll through the entire channel and end up back where it started. What goes around comes around.