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 A020760 Decimal expansion of 1/sqrt(3). 22
 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 (list; constant; graph; refs; listen; history; text; internal format)
 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 n-dimensional geometric shape. For 3D cuboids it is A165952. - Stanislav Sykora, Mar 07 2016 LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 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 1/sqrt(3) = 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 STATUS approved

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