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"How many M&M's are in this jar? Hint: It's all in the packing," by Michael Stroh. The Baltimore Sun, 16 February 2004.
Several recent articles have covered a team's research showing that oblate spheroids in the shape of M&M candies pack more effeciently than spheres. Stroh's piece discusses the mathematics behind the story. The lead researcher in the M&M experiements is Salvatore Torquato, professor of chemistry at Princeton University. Stroh notes that mathematicians started working 400 years ago on "the packing problem [which] has played a role in scientific endeavors ranging from the study of human cells to the design of high-speed computer modems." The article gives an overview of the "cannonball question" allegedly posed by Sir Walter Raleigh ("Was it possible to calculate how much ammunition he had in each pile [on the deck of his ship], based solely on its shape and size?"). He got help from a mathematician, who solved that problem in 1591 and then investigated how the cannonballs could be arranged in the ship's hold with the least wasted space. German mathematician Johannes Kepler conjectured a solution that was proven to be correct 387 years later, in 1998, by mathematician Thomas Hales. Mathematicians have studied the efficiency of randomly-packed versus pyramid-stacked spheres as well, and the new research shows that oblate spheroids pack the most densely: "The M&M's filled 68% of the container---four percentage points more than the randomly-packed ball bearings would." This new research, published in Science, "could lead to everything from advanced new manufacturing materials to more economical ways of packing and shipping goods."
The article presenting this research is:
"Improving the Density of Jammed Disordered Pakcings Using Ellipsoids," by Aleksander Donev, Ibrahim Cisse, David Sachs, Evan A. Variano, Frank H. Stillinger, Robert Connelly, Salvatore Torquato, P.M. Chalkin, Science, 13 February 2004.
See also the following news reports:
"Packing in the Spheres," by David A. Weitz, Science, 13 February 2004;
"Candy Science," by P. Weiss, Science news, 14 February 2004
"After Packing M&M's Together, Scientists Like What They See," by Kenneth Chang, The New York Times, 13 February 2004;
"Why there's always room for a few extra chocs," New Scientist, 21 February 2004, page 15.
--- Annette Emerson