I have been making sculpture since 1971 when I took an evening sculpture course and discovered I loved carving both wood and stone. I was mainly influenced by Barbara Hepworth and Henry Moore. For about twenty five years my carving was therapy from mathematical research and did not relate to mathematics. However, I started organizing art/math conferences in 1992 and this resulted in mathematics gradually influencing my subject matter. About four years ago I started making geometric steel sculpture. Recently I started making Mobius bands by twisting a relatively narrow steel rectangle and welding three together. I switched to aluminum since it heats up faster and is easier to twist.
Triple Twist Mobious Band
9 x 9 x 2 inches
I start with three aluminum rectangles each 2 inches wide, quarter inch thick, and ten inches long. A rectangle is mounted vertically in a vice and a three foot steel bar is clamped horizontally to the top edge. After heating the rectangle, the steel bar is used to twist the rectangle a half turn. The three twisted rectangles are then welded end to end in the shape of a triangle. This is a triple twist Mobius band. The process is completed by grinding, filing, and sanding. Note that the edge of the band is a closed curve in space with three alternating crossings (one crossing per twist); hence the edge of the band is a trefoil knot.