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 number of third degree.

It has decimal digits 1.25992104989... (OEIS A002580).

Its continued fraction is [1, 3, 1, 5, 1, 1, 4, 1, 1, 8, 1, 14, 1, ...] (OEIS A002945).

REFERENCES:

Conway, J. H. and Guy, R. K. "Three Greek Problems." In The Book of Numbers. New York: Springer-Verlag, pp. 192-194, 1996.

Lang, S. and Trotter, H. "Continued Fractions for Some Algebraic Numbers." J. reine angew. Math. 255, 112-134, 1972.

Sloane, N. J. A. Sequences A002580/M1354 and A002945/M2220 in "The On-Line Encyclopedia of Integer Sequences."

Uhler, H. S. "Many-Figure Approximations For , , , and  with  Data." Scripta Math. 18, 173-176, 1952.

Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, pp. 33-34, 1986.