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Math in the Media 1199
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November 1999

• The crumpling catastrophe
• How to slice a tort?
• Beautiful dynamics
• The crumpling catastrophe: push a flat sheet of paper into a coffee filter holder. You will see conical dislocations in crumpling'' as described in an article with that title in the September 2, 1999 Nature by Cerda, Chaieb, Melo and Mahadevan, a Universidad de Santiago de Chile-MIT team. They report a quantitative description of the shape, response and stability of conical dislocations, the simplest type of topological crumpling deformation.'' Here is a picture of the distortion undergone by the paper:

Reprinted by permission from Nature Nature 401, 46 - 49 (1999)

It is interesting to compare this image with a picture of the cusp catastrophe:''

The cusp catastrophe." The orange-yellow plane is mapped to the blue-green plane by (x,y)-->(x3 - 2xy,y).
Folding occurs along the line y = (3/2)x2, and crumpling at the point (0,0).

The study of conical dislocations gives a geometrical meaning, with curvatures related to the physical parameters of the experiment, to this purely topological concept.

How to slice a tort? A new algorithm devised by NYU politics professor Steven Brams and Union College math professor Alan Taylor gives a method for arbitrating any dispute in which goods are to be divided,'' according to Larissa McFarquhar in a Talk of the Town piece in the August 19 New Yorker. The patented algorithm allows a distribution of most of the goods in such a way as to divide evenly the satisfaction each disputant derives from the partition, with the round-off settled by cash if necessary. The New Yorker worried about how spite'' would perturb the calculation in a particularly acrimonious divorce, for example, but this worry seems to come from too material an interpretation of goods.'' For more information on Fair Division problems consult pages at University of Alabama -Center for Teaching and Learning, University of Colorado - Discrete Math Project, or Cedarville College.

Beautiful dynamics. "Persistent patterns in transient chaotic fluid mixing" in the October 21, 1999 Nature describes an elegant set of experiments in which a thin layer of fluid was stirred so as to create a time-periodic velocity field. Calculations had predicted the development of persistent spatial patterns, whose amplitude (contrast) decays slowly with time but without change of form.'' Here is a snapshot of one of the experiments:

Reprinted by permission from Nature 401, 770 - 772 (1999)