Science

The Poppy-Seed Bagel Theorem

By Brij Singh ⋅ December 1, 2004 ⋅  Email This Post ⋅  Print This Post ⋅ Post a comment

On why mathematics is will always cool:

Recently, Hardin and Saff analyzed a method for generating large
numbers of points that are spread with near uniformity over practically
any surface of any dimension. Their effort is described in the cover
article of the November issue of Notices of the American Mathematical
Society.

The procedure has a surprising number of applications. Among other
things, it comes in handy when trying to digitize curved surfaces for
computer graphics and animations with greater efficiency, in placing
the elements of a sonar net on the ocean bottom in the best locations
to detect the presence of submarines, and in testing radar systems in
aircraft to ensure uniform coverage.

Their theorems also help explain a variety of natural phenomena. They
describe some well known patterns such as that of spores on spherical
pollen grains and the way electrons distribute themselves on the
surface of a sphere.

They also promise to provide new insights into the nature of more
complex patterns such as the surface structures of some viruses and the
locations of cracks in crystalline materials. "It’s a nice mix of
mathematical theory, computation and physics," says Hardin.