Gardner's use of the expressions "Cut The queen is "Mathematically, perhaps a torus" (93),
defined as "a surface having the shape of a doughnut."
A "toroid" is "A surface generated by a closed
curve rotating about, but not intersecting or containing, an
axis in its own plane" ( I am certainly no mathematician, but I am told that in calculus one can determine the volume of a non-uniform shape (for instance, a drinking glass that begins narrow on the bottom and becomes gradually wider to the top) by imagining that the shape consists of any number of disks (the more disks, the more accurate the measure) piled upon each other within the form (somewhat as in the following crude graphic): The form's volume would consist of the sum of the volume of each of the imagined disks. Points (or "Cuts") A and B in this illustration represent the extreme limits of the form from the widest (A) to the narrowest (B). Now, if Gardner (and/or Grendel) has something like this in
mind, what do we find? Just before Cut Another element that seems to support this movement from the
broad Cut If any reader has further thoughts, corrections, or additions to this subject, please contact me. Please see the excellent graphics (and very technical explanation) of the torus at the MathWorld site. |