duplication of the cube: see geometric problems of antiquity geometric problems of antiquity, three famous problems involving elementary geometric constructions with straight edge and compass, conjectured by the ancient Greeks to be impossible but not proved to be so until modern times.
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Duplication of the Cube
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Duplication of the Cube
a classic problem of geometric construction dating back to ancient times. It is the problem of constructing a cube whose volume is twice that of a given cube. The problem is sometimes called the Delian problem because, according to legend, an oracle said that a plague on Delos, an island in the Aegean Sea, would come to an end if a certain cubic altar were doubled without changing its shape. The problem reduces to the construction of a line segment whose length is equal to 
. As was proved in the 19th century, such a construction cannot be carried out with compasses and straightedge alone. The problem can be solved by making use of, for example, conic sections.
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