

A157697


Decimal expansion of sqrt(2/3).


8



8, 1, 6, 4, 9, 6, 5, 8, 0, 9, 2, 7, 7, 2, 6, 0, 3, 2, 7, 3, 2, 4, 2, 8, 0, 2, 4, 9, 0, 1, 9, 6, 3, 7, 9, 7, 3, 2, 1, 9, 8, 2, 4, 9, 3, 5, 5, 2, 2, 2, 3, 3, 7, 6, 1, 4, 4, 2, 3, 0, 8, 5, 5, 7, 5, 0, 3, 2, 0, 1, 2, 5, 8, 1, 9, 1, 0, 5, 0, 0, 8, 8, 4, 6, 6, 1, 9, 8, 1, 1, 0, 3, 4, 8, 8, 0, 0, 7, 8, 2, 7, 2, 8, 6, 4
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OFFSET

0,1


COMMENTS

Height (from a vertex to the opposite face) of regular tetrahedron with unit edge.  Stanislav Sykora, May 31 2012
The eccentricity of the ellipse of minimum area that is circumscribing two equal and externally tangent circles (Kotani, 1995).  Amiram Eldar, Mar 06 2022
The standard deviation of a roll of a 3sided die.  Mohammed Yaseen, Feb 23 2023


REFERENCES

L. B. W. Jolley, Summation of Series, Dover, 1961, eq. (168) on page 32.


LINKS

Jisho Kotani, Problem 2053, Crux Mathematicorum, Vol. 5, No. 1 (1995), p. 202; Solution to Problem 2053, by David Hankin, ibid., Vol. 22, No. 4 (1996), pp. 187188.


FORMULA

Equals 1  (1/2)/2 + (1*3)/(2*4)/2^2  (1*3*5)/(2*4*6)/2^3 + ... [Jolley]
Equals Sum_{n>=0} (1)^n*binomial(2n,n)/8^n = 1/A115754. Averaging this constant with sqrt(2) = A002193 = Sum_{n>=0} binomial(2n,n)/8^n yields A145439.
Has periodic continued fraction expansion [0, 1, 4; 2, 4]. (End)


EXAMPLE

0.8164965809277260327324280249...


MAPLE

evalf(sqrt(2/3)) ;


MATHEMATICA



PROG



CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



