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A104956 Decimal expansion of the area of the regular hexagon with circumradius 1. 16
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-Fran├žois Alcover, Dec 19 2016

LINKS

Table of n, a(n) for n=1..105.

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

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 May 27 16:49 EDT 2017. Contains 287207 sequences.