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A104955
Decimal expansion of the area of the regular 5-gon (pentagon) of circumradius = 1.
6
2, 3, 7, 7, 6, 4, 1, 2, 9, 0, 7, 3, 7, 8, 8, 3, 9, 3, 0, 2, 9, 1, 0, 9, 8, 3, 3, 3, 4, 4, 8, 4, 5, 5, 3, 5, 8, 5, 1, 4, 2, 4, 6, 5, 8, 5, 3, 1, 4, 3, 7, 5, 5, 5, 6, 1, 1, 8, 2, 6, 4, 1, 1, 1, 0, 7, 5, 3, 8, 2, 9, 2, 5, 2, 1, 2, 9, 8, 3, 7, 5, 4, 2, 9, 6, 9, 8, 2, 0, 2, 7, 4, 2, 7, 0, 2, 8, 4, 5, 4, 1, 8, 9, 7, 4
OFFSET
1,1
COMMENTS
Equivalently, the area in the complex plane of the smallest convex set containing all order-5 roots of unity.
LINKS
Eric Weisstein et al., Root of Unity.
Eric Weisstein's World of Mathematics, de Moivre Number.
FORMULA
Equals (5*sqrt((5 + sqrt(5))/2))/4.
EXAMPLE
2.377641290737883930291098333448455358514246585314375556118264111075382925212...
MATHEMATICA
Floor[n/2]*Sin[(2*Pi)/n] - Sin[(4*Pi*Floor[n/2])/n]/2 /. n -> 5
RealDigits[(5(Sqrt[(5+Sqrt[5])/2]))/4, 10, 120][[1]] (* Harvey P. Dale, Jul 21 2013 *)
PROG
(PARI) (5*sqrt((5 + sqrt(5))/2))/4 \\ Michel Marcus, Feb 24 2023
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Joseph Biberstine (jrbibers(AT)indiana.edu), Mar 30 2005
STATUS
approved