# Squaring the circle problem There are two different problems related to squaring of the circle. The first was suggested by Alfred Tarski in 1925 that ask if a circle can be transformed to square using scissors dissection. In 1963, Dublin, Hirsch and Karush have shown that it is not possible. In 1990, Laczkovich showed that it could be done using [[Equidecomposability]] technique. The proof uses the [[The Axiom of Choice]] so it is not constructive and Laczkovich estimates it will require $10^{50}$ pieces. The second problem is the classical problem from antiquity of constructing a square with the same area as a given circle using rule and compass. The area of a circle with unit radius is equal to $\pi$ and so the side of the required square is $\sqrt{\pi}$ . In 1880, Ferdinand Lindemann proved that $\pi$ is a transcendental number and it easily proven that using rule and compass one can only generate algebraic numbers i.e., non-transcendental. Reference:[[@The pea and the sun]] #math ## Created 2024-03-03 06:14