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%I #36 Aug 21 2023 11:22:12
%S 7,6,9,4,2,0,8,8,4,2,9,3,8,1,3,3,5,0,6,4,2,5,7,2,6,4,4,0,0,9,2,2,7,4,
%T 5,6,0,0,1,6,7,5,5,3,5,8,8,4,4,4,8,1,0,6,7,5,9,7,8,9,0,6,2,5,9,3,7,1,
%U 5,8,2,2,1,2,3,7,7,2,7,2,9,6,1,3,6,4,8,4,3,0,4,1,6,7,7,6,3,5,8,8,1,7,9,7,6
%N Decimal expansion of the area of the regular 10-gon (decagon) of edge length 1.
%C An algebraic number with degree 4 and denominator 2; minimal polynomial 16x^4 - 1000x^2 + 3125. - _Charles R Greathouse IV_, Apr 25 2016
%C This equals in a regular pentagon inscribed in a unit circle with vertices V0 = (x, y) = (1, 0), and V1..V4 in the counterclockwise sense, one tenth of the y-coordinate of the midpoint of side (V1,V2), named M1: M1_y = (2*sqrt(3 - phi) + sqrt(7 - 4*phi))/4 = sqrt(3 + 4*phi)/4. The x-coordinate is M1_x = -1/4. - _Wolfdieter Lang_, Jan 09 2018
%H Chai Wah Wu, <a href="/A178816/b178816.txt">Table of n, a(n) for n = 1..10001</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Decagon">Decagon</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Regular_polygon">Regular polygon</a>
%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F Digits of 5*sqrt(5+2*sqrt(5))/2 = (5/2)*sqrt(3 + 4*phi), with phi from A001622.
%e 7.69420884293813350642572644009227456001675535884448106759789062593715...
%e sqrt(3 + 4*phi)/4 = 0.769420884293813350642572644009227456001675535884... - _Wolfdieter Lang_, Jan 09 2018
%p evalf[120](5*sqrt(5+2*sqrt(5))/2); # _Muniru A Asiru_, Jan 22 2019
%t RealDigits[5*Sqrt[5+2*Sqrt[5]]/2, 10, 100][[1]]
%o (PARI) 5*sqrt(2*sqrt(5)+5)/2 \\ _Charles R Greathouse IV_, Apr 25 2016
%o (Magma) SetDefaultRealField(RealField(100)); 5*Sqrt(2*Sqrt(5)+5)/2; // _G. C. Greubel_, Jan 22 2019
%o (Sage) numerical_approx(5*sqrt(2*sqrt(5)+5)/2, digits=100) # _G. C. Greubel_, Jan 22 2019
%Y Cf. Areas of other regular polygons: A120011, A102771, A104956, A178817, A090488, A256853, A256854, A178809.
%Y Cf. A001622.
%K nonn,cons,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jun 16 2010
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