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Delian Constant

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The number 2^(1/3)=RadicalBox[2, 3] (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).

See also

Cube, Cube Duplication, Cube Root, Geometric Construction, Geometric Problems of Antiquity, Pythagoras's Constant

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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 RadicalBox[2, 3], RadicalBox[3, 3], RadicalBox[4, 3], and RadicalBox[9, 3] with chi^2 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.

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Delian Constant

Cite this as:

Weisstein, Eric W. "Delian Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DelianConstant.html

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