Quadrature of the circle

Quadrature of the circle is a classical problem from ancient mathematics that involves constructing, with only a compass and straightedge, a square that has the same area as a given circle. Essentially, it's about finding a precise way to recreate the circle's area in square form without approximation. Mathematically, it was proven impossible because the value pi (π), which relates the circle’s diameter to its circumference, is transcendental, meaning it cannot be constructed exactly using these tools. Thus, quadrature of the circle is a famous example illustrating the limitations of geometric constructions.