„The solution of the problem of squaring the circle by compass and straightedge requires the construction of the number √π. If √π is constructible, it follows from standard constructions that π would also be constructible.“

„In 1882, the task was proven to be impossible, as a consequence of the Lindemann –Weierstrass theorem which proves that pi (π) is a transcendental, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients.“

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related to the topic: How people find out pi? ; Area and circumference of a circle