A JAR of M&M chocolate treats turns out to have a peculiar mathematical property. The ellipsoid-shaped sweets pack far more densely into the jar than spherical objects like marbles.
It has long been known, at least to mathematicians, that if you put marbles into a jar and gently shake them to pack in as many as possible, the marbles will occupy no more than about 64 per cent of the jar鈥檚 volume. This is called random close packing.
But when physicist Salvatore Torquato of Princeton University in New Jersey and his colleagues did this with M&Ms, they found the randomly packed sweets approached a packing density of nearly 71 per cent. Using computer simulations, they found that by tweaking the dimensions of the ellipsoid, the packing density could be increased to nearly 74 per cent (Science, vol 303, p 990).
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In random packing, the greatest packing density is obtained when the contents are mechanically stable. Ellipsoids, it turns out, become stable when they are in contact with many more neighbours than happens with spheres.
