Is It Actually Impossible to “Square the Circle?”
Geometry students are taught that squaring the circle — using a compass and straightedge to draw a square with the same area as a given circle — is impossible. But in February 2022, a trio of mathematicians who couldn’t resist an impossible challenge presented the closest solution yet for the problem.
Squaring the circle has a history of failed attempts dating back at least to the ancient Greeks. And in 1882, French mathematician Carl Louis Ferdinand von Lindemann proved that pi is transcendental, which means, among other things, that it’s impossible to draw a line of that length. Since the area of a circle depends on pi and the area of a square doesn’t, a solution was provably impossible.
But what if you abandon the compass and straightedge? Nearly a century ago, mathematicians asked whether it was possible to break a circle into pieces that could be reassembled into a square of the same area, with no compass or straightedge involved. Then in 1989, Hungarian mathematician Miklòs Laczkovich proved that it was theoretically possible, but the pieces would be so complicated as to be unmeasurable.