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Decimal expansion of (1/2)*sqrt(7 + phi), with the golden section from A001622.
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%I #10 Jan 15 2018 03:28:28

%S 1,4,6,7,8,2,4,4,0,9,5,2,1,6,1,3,6,2,8,0,9,8,1,6,3,7,2,6,4,6,7,1,2,1,

%T 3,3,7,5,4,2,5,6,5,5,5,9,8,8,8,4,2,0,0,2,0,5,1,0,2,9,9,2,9,7,5,2,3,2,

%U 9,4,3,8,3,3,9,9,6,9,5,4,4,9,3,8,2,1,4,5,9,9,3,8,1,8,3,4,2,7

%N Decimal expansion of (1/2)*sqrt(7 + phi), with the golden section from A001622.

%C In a regular pentagon inscribed in a unit circle this equals the second largest distance between a vertex and a midpoint of a side. The shortest such distance is (1/2)*sqrt(3 - phi) = (1/2)*A182007 = 0.58778525229..., and the longest 1 + phi/2 = (1/2)*(2 + phi) = (1/2)*A296184 = 1.80901699437...

%F (1/2)*sqrt(7 + phi). From the comment on the pentagon above this results from sqrt((5/4)^2 + (sqrt(3 - phi)/2 + sqrt(7 - 4*phi)/4)^2).

%e 1.467824409521613628098163726467121337542565559888420020510299297523294383...

%t First@ RealDigits[Sqrt[7 + GoldenRatio]/2, 10, 98] (* _Michael De Vlieger_, Jan 13 2018 *)

%Y Cf. A001622, A182007, A296184.

%K nonn,cons,easy

%O 1,2

%A _Wolfdieter Lang_, Jan 08 2018