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The number 
 (the Cube Root of 2) which is to be constructed in the Cube Duplication problem.  This
number is not a Euclidean Number although it is an 
Algebraic of third degree.
References
Conway, J. H. and Guy, R. K.  ``Three Greek Problems.''  In The Book of Numbers.  New York: Springer-Verlag,
  pp. 192-194, 1996.