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 A104956 Decimal expansion of the area of the regular hexagon with circumradius 1. 17
 2, 5, 9, 8, 0, 7, 6, 2, 1, 1, 3, 5, 3, 3, 1, 5, 9, 4, 0, 2, 9, 1, 1, 6, 9, 5, 1, 2, 2, 5, 8, 8, 0, 8, 5, 5, 0, 4, 1, 4, 2, 0, 7, 8, 8, 0, 7, 1, 5, 5, 7, 0, 9, 4, 2, 0, 8, 3, 7, 1, 0, 4, 6, 9, 1, 7, 7, 8, 9, 9, 5, 2, 5, 3, 6, 3, 2, 0, 0, 0, 5, 5, 6, 2, 1, 7, 1, 9, 2, 8, 0, 1, 3, 5, 8, 7, 2, 8, 6, 3, 5, 1, 3, 4, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, the area in the complex plane of the smallest convex set containing all order-6 roots of unity. Subtracting 2.5 (i.e., dropping the first two digits) we obtain 0.09807.... which is a limiting mean cluster density for a bond percolation model at probability 1/2 [Finch]. - R. J. Mathar, Jul 26 2007 This constant is also the minimum radius of curvature of the exponential curve (occurring at x = -log(2)/2 = -0.34657359...). - Jean-François Alcover, Dec 19 2016 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 S. R. Finch, Several Constants Arising in Statistical Mechanics, Annals Combinat. vol 3 (1999) issue (2-4) pp. 323-335. Eric Weisstein et al., Root of Unity Eric Weisstein's World of Mathematics, de Moivre Number Eric Weisstein's World of Mathematics, Twenty-Vertex Entropy Constant Wikipedia, Hexagon Wikipedia, Regular polygon FORMULA Equals (3*sqrt(3))/2, that is, 2*A104954. EXAMPLE 2.59807621135331594029116951225880855041420788071557094208371046917789952536320... MATHEMATICA Floor[n/2]*Sin[(2*Pi)/n] - Sin[(4*Pi*Floor[n/2])/n]/2 /. n -> 6 RealDigits[(3*Sqrt[3])/2, 10, 50][[1]] (* G. C. Greubel, Jul 03 2017 *) PROG (PARI) 3*sqrt(3)/2 \\ G. C. Greubel, Jul 03 2017 CROSSREFS Cf. A002194, A104954, A104955, A104957. Cf. Areas of other regular polygons: A120011, A102771, A178817, A090488, A256853, A178816, A256854, A178809. Sequence in context: A089578 A020852 A053477 * A020820 A111290 A129140 Adjacent sequences:  A104953 A104954 A104955 * A104957 A104958 A104959 KEYWORD nonn,cons AUTHOR Joseph Biberstine (jrbibers(AT)indiana.edu), Mar 30 2005 STATUS approved

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Last modified August 18 20:05 EDT 2018. Contains 313837 sequences. (Running on oeis4.)