Squaring the circle

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A circle and a square, with the same area.

Squaring the circle is a problem of geometry. The problem is to construct a square that has the same area as the unit circle, only by using a compass and straightedge construction method. Some people also call this problem the quadrature of the circle.

This is not about a circle with corners like a square. It is a problem like squaring a triangle. It is easy to construct a square with the same area as a triangle. Squaring the circle is related to the other ancient problems which have been proved impossible, squaring the cube and trisecting the angle.

In 1882, Ferdinand von Lindenmann proved that this is impossible because it is impossible to calculate √π exactly, which is a transcendental number.