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Wrap Not, Waste Not

A mathematical equation may help cut down on holiday waste.
December 6, 2007

Each year, reams and reams of wrapping paper are wasted as gift givers tend to overestimate the amount of gift wrap required to festoon their packages. To cut down on all this holiday paper waste, a British mathematician at the University of Leicester has devised a formula for how to most efficiently wrap a present of any shape and size.

Credit: Nicolas Raymond

In a university press release, the equation’s originator, postgraduate student Warwick Dumas, says,

“We have tested different methods of wrapping and our investigations showed that … cutting the right size of paper will allow consumers to wrap presents in the least amount of time and achieve a classy result.”

The formula, which can be applied to any box-shaped item, goes like this:

Area = 2(ab+ac+bc+c²)

“To explain in the most simplistic terms, the minimal area of paper needed to wrap a box-shaped gift is twice the sum of the height times the width, the width times the depth and the height times the depth, plus twice the square of the depth,” says Dumas.

In multiple tests, Dumas found that wrapping cubic-shaped objects diagonally used up more paper than wrapping along the edges–except when the object has a square base. Then, the best method is to wrap diagonally, so that the flaps only just meet.

The same equation for box-shaped items may be used to wrap cylindrical gifts whose radius is greater than 87 percent of their height (for example, a squat tin of cookies). Taller cylinders (e.g., tubes of socks) may be best wrapped via a rolling method.

Dumas has teamed up with Bluewater, a major shopping center based in the United Kingdom, to help shoppers reduce their “gift-wrapping footprint.” Bluewater plans to hold workshops throughout the holiday season to teach shoppers the ecofriendly wrapping equation.

Of course, minimizing the extra scratch paper you’ll need in order to make your gift-wrapping calculations is another problem entirely.

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