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The geometry of M&M's

An experimental packing of M&Ms. [Image Science]
Click here for a high resolution photograph.

If you had two containers, one filled with M&M's and the other filled with M&M-sized gumballs, which container would hold more objects?

Most scientists would pick the gumballs, because they figure that spheres fit together more closely than other shapes do. Aleksandar Donev of Princeton University in Princeton, N.J., and his colleagues have just discovered, however, that oval-shaped objects like M&M's can actually jam together more tightly than spheres do.

Computer-generated packing. [Image Science]
Click here for a high resolution photograph.

Their study appears in the 13 February issue of the journal Science.

This information is useful for a lot more than just figuring out whether you'll get more M&M's or gumballs for your money. Understanding how to pack objects efficiently is important for store-owners, packagers and shippers. Researchers have been studying this issue for centuries - although they've typically just studied spheres and not other shapes.

Donev's team compared the density of round ball-bearings and M&M's, packed without any particular order into different containers. They found much less empty space among the M&M's than among the ball-bearings. The researchers also used an MRI scan (which they give in the hospital to see inside patients' bodies) to look at a cross-section of the M&M-filled container. This information helped them figure out a mathematical equation that describes how oval shapes pack together.


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