Squaring the circle, the construction of a square with the same area as a given circle, is one of the three construction problems that the Greeks posed but were unable to solve. Unlike trisecting the angle and doubling the cube, where the impossibility follows from properties of the roots of polynomials, the impossibility of squaring the circle follows from the transcendentality of 𝜋: it is not the root of any polynomial with rational coefficients. This is a difficult theorem that was proved in 1882 by Carl von Lindemann.
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Ben-Ari, M. (2022). Squaring the Circle. In: Mathematical Surprises. Springer, Cham. https://doi.org/10.1007/978-3-031-13566-8_3
Publisher Name: Springer, Cham
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