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A258403 Decimal expansion of the area of the regular 10-gon (decagon) of circumradius = 1.

%I A258403 #43 Feb 16 2025 08:33:25
%S A258403 2,9,3,8,9,2,6,2,6,1,4,6,2,3,6,5,6,4,5,8,4,3,5,2,9,7,7,3,1,9,5,3,6,3,
%T A258403 8,4,2,9,8,8,2,6,2,1,8,8,2,1,5,7,2,9,9,5,5,3,6,1,3,6,2,4,0,3,7,8,6,3,
%U A258403 9,2,3,7,0,8,1,1,7,5,9,7,8,7,5,4,2,5,2,0,2,4,9,3,1,3,7,0,6,6,7,9,8
%N A258403 Decimal expansion of the area of the regular 10-gon (decagon) of circumradius = 1.
%C A258403 Quartic number of degree 4 and denominator 2; minimal polynomial 16x^4 - 500x^2 + 3125. - _Charles R Greathouse IV_, Apr 20 2016
%H A258403 Chai Wah Wu, <a href="/A258403/b258403.txt">Table of n, a(n) for n = 1..10001</a>
%H A258403 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Decagon.html">Decagon</a>
%H A258403 Wikipedia, <a href="http://en.wikipedia.org/wiki/Decagon">Decagon</a>
%F A258403 Equals (5/2)*sqrt((5-sqrt(5))/2).
%F A258403 Area formulas from triangle to dodecagon, with circumradius 1:
%F A258403    n-gon    area(n) = (1/2)*n*sin(2*Pi/n)
%F A258403    3-gon    (3*sqrt(3))/4
%F A258403    4-gon    2
%F A258403    5-gon    (5/4)*sqrt((5+sqrt(5))/2)
%F A258403    6-gon    (3*sqrt(3))/2
%F A258403    7-gon    (7/2)*cos((3*Pi)/14)
%F A258403    8-gon    2*sqrt(2)
%F A258403    9-gon    (9/2)*sin((2*Pi)/9)
%F A258403   10-gon    (5/2)*sqrt((5-sqrt(5))/2)
%F A258403   11-gon    (11/2)*sin((2*Pi)/11)
%F A258403   12-gon    3
%F A258403 This constant is (5/2)*A182007. - _Wolfdieter Lang_, May 08 2018
%e A258403 2.9389262614623656458435297731953638429882621882157299553613624...
%t A258403 RealDigits[(5/2)*Sqrt[(5 - Sqrt[5])/2], 10, 101] // First
%o A258403 (PARI) (5/2)*sqrt((5 - sqrt(5))/2) \\ _Michel Marcus_, May 29 2015
%Y A258403 Cf. A104954 (triangle), A104955 (pentagon), A104956 (hexagon), A104957 (heptagon).
%Y A258403 Cf. A178816 (area of decagon with edge length 1). A182007.
%K A258403 nonn,cons,easy
%O A258403 1,1
%A A258403 _Jean-François Alcover_, May 29 2015