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Math Trek

Squaring Circles

By
5:53pm, October 26, 2004

There's no telling where thoughts about a seemingly simple, even trivial, question may lead.

Consider the problem of turning a circle into a square. Cut a circle out of a sheet of paper. Then cut the circle into pieces so that the pieces, when fitted back together, form a square having the same area as the original circle.

The task seems impossible: How do you get rid of the curves?

But there is a mathematical solution. In 1989, Hungarian mathematician Miklós Laczkovich accomplished the mind-bending feat of proving that it is theoretically possible to cut a circle into a finite number of pieces that can be rearranged into a square.

The problem solved by Laczkovich is related to an ancient riddle known to Archimedes, Euclid, and other Greek scholars. At issue is whether it's possible, with just a ruler and compass, to draw a square with an area equal to that of a

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