

A020760


Decimal expansion of 1/sqrt(3).


24



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

0,1


COMMENTS

If the sides of a triangle form an arithmetic progression in the ratio 1:1+d:1+2d then when d=1/sqrt(3) it uniquely maximizes the area of the triangle. This triangle has approximate internal angles 25.588 degs, 42.941 degs, 111.471 degs.  Frank M Jackson, Jun 15 2011
When a cylinder is completely enclosed by a sphere, it occupies a fraction f of the sphere volume. The value of f has a trivial lower bound of 0, and an upper bound which is this constant. It is achieved iff the cylinder diameter is sqrt(2) times its height, and the sphere is circumscribed to it. A similar constant can be associated with any ndimensional geometric shape. For 3D cuboids it is A165952.  Stanislav Sykora, Mar 07 2016
The ratio between the thickness and diameter of a dynamically fair coin having an equal probability, 1/3, of landing on each of its two faces and on its side after being tossed in the air. The calculation is based on the dynamic of rigid body (Yong and Mahadevan, 2011). See A020765 for a simplified geometrical solution.  Amiram Eldar, Sep 01 2020


LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Ee Hou Yong and L. Mahadevan, Probability, geometry, and dynamics in the toss of a thick coin, American Journal of Physics, Vol. 79, No. 12 (2011), pp. 11951201, preprint, arXiv:1008.4559 [physics.classph], 2010.


FORMULA

Equals 1/A002194.  Michel Marcus, Oct 12 2014
Equals cosine of the magic angle: cos(A195696).  Stanislav Sykora, Mar 07 2016
Equals square root of A010701.  Michel Marcus, Mar 07 2016


EXAMPLE

0.577350269189625764509148780501957455647601751270126876018602326...  Vladimir Joseph Stephan Orlovsky, May 27 2010


MATHEMATICA

RealDigits[N[1/Sqrt[3], 200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)


CROSSREFS

Cf. A002194 (sqrt(3)), A010701 (1/3).
Cf. A002193, A165952, A195696.
Sequence in context: A021638 A258408 A210623 * A225155 A011269 A093723
Adjacent sequences: A020757 A020758 A020759 * A020761 A020762 A020763


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane.


STATUS

approved



