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%I #49 Aug 21 2023 11:22:26
%S 3,6,3,3,9,1,2,4,4,4,0,0,1,5,8,8,9,9,2,5,3,6,1,9,3,0,0,7,6,0,0,2,2,0,
%T 5,7,8,7,3,5,0,1,0,3,6,1,5,9,5,4,4,4,9,1,7,1,4,5,9,8,0,4,0,9,5,1,0,2,
%U 9,9,8,5,2,3,6,3,0,4,6,0,0,5,5,6,2,7,3,0,7,1,5,2,9,5,8,1,0,8,9,4,3,7,1,0,4
%N Decimal expansion of the area of the regular 7-gon (heptagon) of edge length 1.
%H G. C. Greubel, <a href="/A178817/b178817.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Heptagon">Heptagon</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Regular_polygon">Regular polygon</a>
%H <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>
%F Equals (7/4) * cot(Pi/7).
%F From _Michal Paulovic_, Dec 27 2022: (Start)
%F Equals 7 / (4 * tan(Pi/7)) = 7 / (4 * A343058).
%F Equals sqrt(7/3 * (35 + 2 * 196^(1/3) * ((13 - 3 * sqrt(3) * i)^(1/3) + (13 + 3 * sqrt(3) * i)^(1/3)))) / 4.
%F Equals sqrt(7/4) * sqrt(35/12 + (637/54 - sqrt(-2401/108))^(1/3) + (637/54 + sqrt(-2401/108))^(1/3)).
%F (End)
%F A root of the polynomial 4096*x^6 - 62720*x^4 + 115248*x^2 - 16807. - _Joerg Arndt_, Jan 02 2023
%e 3.63391244400158899253619300760022057873501036159544491714598040951029...
%p evalf[120]((7/4)*cot(Pi/7)); # _Muniru A Asiru_, Jan 22 2019
%t RealDigits[7*Cot[Pi/7]/4, 10, 100][[1]]
%o (PARI) p=7; a=(p/4)*cotan(Pi/p) \\ Set realprecision in excess. - _Stanislav Sykora_, Apr 12 2015
%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); 7*Cot(Pi(R)/7)/4; // _G. C. Greubel_, Jan 22 2019
%o (Sage) numerical_approx(7*cot(pi/7)/4, digits=100) # _G. C. Greubel_, Jan 22 2019
%Y Cf. A178818, A343058.
%Y Cf. Areas of other regular polygons: A120011, A102771, A104956, A090488, A256853, A178816, A256854, A178809.
%K nonn,cons,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jun 16 2010
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