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A248413 Decimal expansion of theta_1, one of the angles associated with the bow-and-arrow configuration used in the 2-arc smallest length problem. 3

%I #7 Oct 06 2014 13:08:11

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

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

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

%N Decimal expansion of theta_1, one of the angles associated with the bow-and-arrow configuration used in the 2-arc smallest length problem.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.11 Beam detection constants, p. 516.

%H <a href="/A248413/a248413.gif">Bow-and-arrow configuration</a> [From the book by Steven Finch]

%F theta_1 = 4*arctan(sqrt(x1)), where x1 is the second smallest positive root of x^10 + 65*x^9 - 2139*x^8 + 20476*x^7 - 78054*x^6 + 126214*x^5 - 78054*x^4 + 20476*x^3 - 2139*x^2 + 65*x + 1.

%e 1.286511267631012300826788540037078935529828319168295...

%t x1 = Root[x^10 + 65*x^9 - 2139*x^8 + 20476*x^7 - 78054*x^6 + 126214*x^5 - 78054*x^4 + 20476*x^3 - 2139*x^2 + 65*x + 1, x, 4]; theta1 = 4*ArcTan[Sqrt[x1]]; RealDigits[theta1, 10, 103] // First

%Y Cf. A248414 (theta_2), A248415 (length upper bound).

%K cons,nonn

%O 1,2

%A _Jean-François Alcover_, Oct 06 2014

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