Cube Duplication

Also called the Delian Problem or Duplication of the Cube. A classical problem of antiquity which, given theEdge of a Cube, requires a second Cube to be constructed having double theVolume of the first using only a Straightedge and Compass.

Under these restrictions, the problem cannot be solved because the Delian Constant (the required Ratioof sides of the original Cube and that to be constructed) is not a Euclidean Number. The problem can be solved,however, using a Neusis Construction.

References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 93-94, 1987.

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 190-191, 1996.

Courant, R. and Robbins, H. ``Doubling the Cube'' and ``A Classical Construction for Doubling the Cube.'' §3.3.1 and 3.5.1 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 134-135 and 146, 1996.

Dörrie, H. ``The Delian Cube-Doubling Problem.'' §35 in 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, pp. 170-172, 1965.

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