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December 01, 2004

The Poppy-Seed Bagel Theorem

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.

December 1, 2004 in Science | Permalink

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