OFFSET
1,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.11 Beam detection constants, p. 516.
LINKS
Bow-and-arrow configuration [From the book by Steven Finch]
FORMULA
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.
EXAMPLE
1.286511267631012300826788540037078935529828319168295...
MATHEMATICA
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
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Jean-François Alcover, Oct 06 2014
STATUS
approved