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Duplication of the Cube

Abstract A tentative construction for an approximate doubling of the volume of a cube which observes the rules of Euclidean geometry and simultaneously displays a structural relationship with another Euclidean impossibility is presented.The construction of a geometric figure which is double the volume of a cube whose side is given, using only compasses and straightedge, has, with the Quadrature of the Circle, the Trisection of an Angle, and the Regular Heptagon, been proved to be impossible. This paper demonstrates a straightforward construction using only compasses and straightedge which achieves two separate approximations to the doubling of the volume of a given cube – one of them extremely accurate – whilst simultaneously displaying a close structural relationship with and derivation from the geometry of the Quadrature of the Circle.