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MatheMUSEments
The Beauty of the Bag
By Ivars Peterson
Muse, January 2006, p. 19.
The humble brown-paper bag that you use to carry groceries
is actually a technological masterpiece that solves many practical
problems. Unlike a plastic bag, it can stand upright by itself; you
don't need an extra hand to hold it open while you fill it. Yet it
folds flat for easy storage.
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A standard brown-paper bag can stand upright. |
It took inventors years to come up with a design that
would behave this way. Early paper bags had "envelope bottoms"
and wouldn't stand up at all. Then in 1867 Margaret Knight invented
a machine that could make the standard bag's rectangular "satchel
bottom" in a series of three folds. Another inventor added the
accordion folds on the sides of the bag.
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The folded form of a standard brown-paper bag. |
A company near Savannah, Georgia, now makes 35 million paper bags
per day, or about 9 billion per year. That's more than 100 bags for
every family in the United States.
A paper bag can be easily folded and unfolded because
it is creased. But these creases are more peculiar than you'd think.
Suppose you made a bag from a very stiff material, such as steel,
and that each crease was some sort of hinge. If the steel bag started
out flat, you wouldn't be able to open it, and if it started out open,
you couldn't fold it flat. The bag could open or close only if the
material could bend, and steel doesn't bend.
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The red lines show where a paper bag is creased. |
Robotics expert Devin Balkcom of Dartmouth College got interested
in grocery bags when he was designing a robot that could do "rigid
origami," origami folding where the paper stays flat. You can
watch his robot fold a paper airplane at
www.cs.dartmouth.edu/~robotics/origami.html.
The film clip will make you laugh—such a big machine concentrating
so hard on such a simple task.
Balkcomm and computer scientists Erik and Martin Demaine of the Massachusetts
Institute of Technology independently observed that rigid grocery
bags wouldn't fold and worked together on finding some mathematical
solutions to this problem. One is to make the bag very short, so it
looks more like a collapsible department-store gift box. That gets
rid of the place on the grocery bag where several creases meet, blocking
collapse. The researchers also figured out how to fold a tall bag
without bending the material, but their method requires a whole bunch
of new creases and doesn't look much like a grocery bag.
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A 'short' bag gets
rid of the place on the grocery bag where several creases meet, blocking
collapse. |
So the next time you use a paper bag, take a closer look at this
wonderful invention. There's a lot to ponder in its simple folds.
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