Squaring the Circle/Historical Note

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Historical Note on Squaring the Circle

The construction of a square with the same area as a given circle, using a compass and straightedge construction, was an exercise that the ancient Greeks failed to succeed in.

This was one of three such problems: the other two being Trisecting the Angle and Doubling the Cube.

There are several techniques available that use other tools, but these were considered unacceptably vulgar to the followers of Plato.

The problem remained unsolved until its impossibility was proved in $1882$ by Ferdinand von Lindemann.