Doubling the Cube by Compass and Straightedge Construction is Impossible

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Theorem

There is no compass and straightedge construction to allow a cube to be constructed whose volume is double that of a given cube.


Proof


Also known as

Some sources refer to the problem of Doubling the Cube as duplicating the cube.

However, the position taken by $\mathsf{Pr} \infty \mathsf{fWiki}$ is that duplication can also mean making an exact copy of, which could cause misunderstanding.


Sources