|
%I #25 Aug 21 2023 10:24:25
%S 1,7,2,0,4,7,7,4,0,0,5,8,8,9,6,6,9,2,2,7,5,9,0,1,1,9,7,7,3,8,8,6,0,9,
%T 5,9,9,4,0,7,3,7,4,1,7,0,0,1,0,1,9,8,3,2,9,2,0,7,0,9,4,7,0,7,0,2,3,8,
%U 6,8,9,9,2,2,0,8,9,6,6,2,3,1,3,3,2,4,4,1,2,4,1,3,8,7,5,8,7,7,4
%N Decimal expansion of area of a regular pentagon with unit edge length.
%H G. C. Greubel, <a href="/A102771/b102771.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Pentagon.html">Pentagon</a>
%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F Equals sqrt(25 + 10*sqrt(5)) / 4.
%F Equals (3*phi+1)*sqrt(3-phi) with the golden section phi = (1 + sqrt(5))/2. - _Wolfdieter Lang_, Jan 25 2013
%F Equals 5/(4*tan(Pi/5)). - _Michel Marcus_, Mar 25 2015
%F Equals (5/4)*sqrt(phi^3/sqrt(5)). - _G. C. Greubel_, Jul 03 2017
%e 1.720477400588966922759011977...
%t RealDigits[(5/4)*Sqrt[GoldenRatio^3/Sqrt[5]], 10, 50][[1]] (* _G. C. Greubel_, Jul 03 2017 *)
%o (PARI) 5/(4*tan(Pi/5)) \\ _Michel Marcus_, Mar 25 2015
%Y Cf. Areas of other regular polygons: A120011, A104956, A178817, A090488, A256853, A178816, A256854, A178809.
%K nonn,cons
%O 1,2
%A Bryan Jacobs (bryanjj(AT)gmail.com), Feb 10 2005
%E Corrected the title. - _Stanislav Sykora_, Apr 12 2015
|
