Doubling the cube

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Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to be impossible to construct by using only a compass and straightedge, but even in ancient times, solutions were known that employed other methods. According to Eutocius, Archytas was the first to solve the problem of doubling the cube, with an ingenious geometric construction. The nonexistence of a compass-and-straightedge solution was finally proven by Pierre Wantzel in 1837. In algebraic terms, doubling a unit cube requires the construction of a line segment of length x, where x3 = 2; in other words, x = 2 3 {\displaystyle {\sqrt[{3}]{2...

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