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Doubling a cube, also known as the problem of the Delian cube, is not possible using only a straightedge and compass. This task involves constructing a cube with a volume twice that of a given cube, which requires finding the length of the edge of the new cube to be the cube root of 2. However, this length cannot be constructed using those tools, as it is not a constructible number. This was proven in the 19th century through the field of algebraic geometry.
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What Greek constructions were never accomplished with only a straightedge and a compass?
Doubling a cube and trisecting any angle
Constructing a cube with double the volume of another cube using only a straightedge and compass was proven possible by advanced algebra.?
No, it is not. In 1837, the French mathematician, Pierre Laurent Wantzel, proved that it was impossible to do so using only compass and straightedge.
Is it possible to construct a cube of twice the volume of a giving cube only using a straightedge and compass?
No, it is not and in 1837 Pierre Wantzel proved this to be the case.
Is it possible to double a cube using a straight edge and compass?
No. This is known to be impossible. For more information, including a proof, check the Wikipedia article on "doubling the cube".
Is doubling a cube possible?
Yes, it is possible.
