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A237558
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Decimal expansion of (1/Pi)*arccos(1/sqrt(3)).
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0
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3, 0, 4, 0, 8, 6, 7, 2, 3, 9, 8, 4, 6, 9, 6, 3, 6, 4, 9, 1, 4, 5, 7, 2, 2, 2, 0, 3, 8, 8, 7, 8, 4, 5, 4, 4, 3, 4, 1, 6, 8, 5, 6, 7, 5, 2, 8, 0, 2, 9, 9, 8, 5, 6, 3, 5, 6, 0, 3, 0, 8, 5, 0, 9, 8, 8, 9, 9, 9, 2, 9, 5, 6, 6, 1, 2, 7, 8, 8, 7, 6, 5, 6, 4, 8, 9, 4, 0, 8, 6, 9, 1, 2, 1, 1, 2, 7, 4, 3
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OFFSET
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0,1
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COMMENTS
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Known to be irrational. If m is a positive integer (1/Pi)*arccos(1/sqrt(m)) is rational iff m=1,2 or 4.
A constant giving the location (x = y) of the thermodynamic center (also called warmest point or "hot spot") of a unit isosceles right triangle. The thermodynamic center is the warmest point in a convex heat conductor with unitary initial temperature and with boundary grounded at zero temperature. The convex heat conductor here considered is the isosceles right triangle x>0, y>0, x+y <= 1. - Jean-François Alcover, Jul 26 2016
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REFERENCES
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M. Aigner and G. M. Ziegler, Proofs from The Book, Chap. 7, p. 40, Springer-Verlag, Berlin, 1999.
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LINKS
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FORMULA
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0 < x < 1/2 maximizing sin(Pi x)*sin(2Pi x), that is x = arctan(sqrt(2)) / Pi, solution to sin(Pi x) = 3 sin(3 Pi x). - Jean-François Alcover, Jul 26 2016
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EXAMPLE
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0.30408672...
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MAPLE
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arccos(1/sqrt(3))/Pi; evalf(%) ; # R. J. Mathar, Aug 02 2016
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MATHEMATICA
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Join[{0}, RealDigits[1/Pi ArcCos[1/Sqrt[3]], 10, 120][[1]]] (* Harvey P. Dale, Feb 22 2015 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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