Squaring the circle was one of the famous Ancient Greek mathematical problems. Although studied intensively for millennia by many brilliant scholars, no solution was ever found. The problem requires the construction of a square having area equal to that of a given circle. This must be done in a finite number of steps, using only ruler and compass.

Taking unit radius for the circle, the area is *π*, so the square must have a side length of √*π*. If we could construct a line segment of length *π*, we could also draw one of length √*π*. However, the only constructable numbers are those arising from a unit length by addition, subtraction, multiplication and division, together with the extraction of square roots.

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