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%I #14 Feb 24 2023 03:10:42
%S 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,
%T 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,
%U 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
%N Decimal expansion of the area of the regular 5-gon (pentagon) of circumradius = 1.
%C Equivalently, the area in the complex plane of the smallest convex set containing all order-5 roots of unity.
%H Chai Wah Wu, <a href="/A104955/b104955.txt">Table of n, a(n) for n = 1..10001</a>
%H Eric Weisstein et al., <a href="http://mathworld.wolfram.com/RootofUnity.html">Root of Unity</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/deMoivreNumber.html">de Moivre Number</a>.
%F Equals (5*sqrt((5 + sqrt(5))/2))/4.
%e 2.377641290737883930291098333448455358514246585314375556118264111075382925212...
%t Floor[n/2]*Sin[(2*Pi)/n] - Sin[(4*Pi*Floor[n/2])/n]/2 /. n -> 5
%t RealDigits[(5(Sqrt[(5+Sqrt[5])/2]))/4,10,120][[1]] (* _Harvey P. Dale_, Jul 21 2013 *)
%o (PARI) (5*sqrt((5 + sqrt(5))/2))/4 \\ _Michel Marcus_, Feb 24 2023
%Y Cf. A104954, A104956, A104957.
%K nonn,cons
%O 1,1
%A Joseph Biberstine (jrbibers(AT)indiana.edu), Mar 30 2005
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