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A255240 Decimal expansion of 1/(2 cos(2 Pi/7)). 1

%I

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

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

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

%N Decimal expansion of 1/(2 cos(2 Pi/7)).

%C This is the decimal expansion of t = 1/rho(7) = 2 + rho(7) - rho(7)^2 with rho(7) = 2*cos(2*Pi/7) the length ratio of the smaller diagonal and the side of a regular heptagon. See A160389 for the decimal expansion of rho(7).

%C t satisfies the cubic equation t^3 - 2*t^2 - t + 1 = 0.

%C t = 1/rho(7) is the slope tan(alpha) appearing in Archimedes's neusis construction of the regular heptagon. The corresponding angle alpha is approximately 29,028 degrees. See the link, Figure 1, also for references.

%H Wolfdieter Lang, <a href="/A255240/a255240.pdf">Archimedes's Construction of the Regular Heptagon.</a>

%F 1/rho(7) = 1/(2*cos(2*Pi/7)) = 0.55495813208...

%Y Cf. A160389, A231187.

%K nonn,cons

%O 1,1

%A _Wolfdieter Lang_, Mar 12 2015

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Last modified February 22 07:03 EST 2020. Contains 332118 sequences. (Running on oeis4.)