This page displays the work that is derived from knots. The edges of all of these pieces if transformed into string, would become knots. The edges are joined to make a surface or a form. I try to actually approach what would be a minimal surface or soap film, but this is only an approximation.
Many of the knots here are actually torus knots. This means that the edges of the forms lie on the surface of a torus (think doughnut). The resultant form may not look like it care from a torus, but indeed they all started as a torus, and were carved away after the knot was laid out on the surface. Torus knots are described (a,b)by the number of times the edge passes through the center hole (a) and the number of times it circles the whole form (b). So a Mathematicians Dream is a 2,3 torus knot and Carnival Mathematica is a 5,3 torus knot. All of the torus knot forms I show here are, by the nature of their form, called non-orientable surfaces. That is, there is only one surface . If you trace your finger around the form it will come back to the starting point. The simplest of these is a moibus strip.
Both Infinite Loop and Inversion are minimal surfaces derived from trefoil knots which is a 3 lobed knot with d crossings. See the minimal surface gallery for more information on minimal surfaces.