Column

  1. Math

    Immersed in Klein Bottles

    “Need a zero-volume bottle? Searching for a one-sided surface? Want the ultimate in nonorientability?” One way to depict a Klein bottle. Computer-generated image by John Sullivan, University of Illinois at Urbana-Champaign Joining the top and bottom of this rectangle produces a cylinder. Matching the arrows of the remaining two sides produces a Klein bottle. One […]

    By Ivars Peterson
  2. Math

    White Narcissus

    The elegant, swooping forms carved out of wood by sculptor Robert Longhurst often resemble gracefully curved soap films that span twisted loops of wire dipped into soapy water. Alhough these abstract sculptures bear an uncanny resemblance to mathematical forms known as minimal surfaces, they emerge from Longhurst’s imagination rather than from mathematics.