

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
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OFFSET

1,1


COMMENTS

Equivalently, the area in the complex plane of the smallest convex set containing all order6 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...).  JeanFrançois 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 (24) pp. 323335.
Eric Weisstein et al., Root of Unity
Eric Weisstein's World of Mathematics, de Moivre Number
Eric Weisstein's World of Mathematics, TwentyVertex 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



