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A358981
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Decimal expansion of Pi/3 - sqrt(3)/4.
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0
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6, 1, 4, 1, 8, 4, 8, 4, 9, 3, 0, 4, 3, 7, 8, 4, 2, 2, 7, 7, 2, 3, 5, 2, 8, 7, 5, 7, 1, 6, 6, 9, 9, 5, 3, 6, 3, 3, 0, 0, 2, 1, 8, 1, 9, 6, 7, 2, 4, 4, 0, 1, 1, 6, 6, 4, 4, 3, 6, 3, 1, 1, 9, 2, 3, 9, 6, 2, 2, 2, 1, 4, 5, 3, 4, 8, 6, 9, 6, 5, 6, 9, 3, 9, 0, 5, 8, 3, 9, 5, 0, 9, 1, 3, 9, 3, 5, 4, 5, 4
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OFFSET
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0,1
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COMMENTS
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The constant is the area of a circular segment bounded by an arc of 2*Pi/3 radians (120 degrees) of a unit circle and by a chord of length sqrt(3). Three such segments result when an equilateral triangle with side length sqrt(3) is circumscribed by a unit circle. The area of each segment is:
A = (R^2 / 2) * (theta - sin(theta))
A = (1^2 / 2) * (2*Pi/3 - sin(2*Pi/3))
A = (1 / 2) * (2*Pi/3 - sqrt(3)/2)
A = Pi/3 - sqrt(3)/4 = (Pi - 3*sqrt(3)/4) / 3 = 0.61418484...
where Pi (A000796) is the area of the circle, and 3*sqrt(3)/4 (A104954) is the area of the inscribed equilateral triangle.
The sagitta (height) of the circular segment is:
h = R * (1 - cos(theta/2))
h = 1 * (1 - cos(Pi/3))
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LINKS
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FORMULA
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EXAMPLE
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0.6141848493043784...
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MAPLE
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evalf(Pi/3-sqrt(3)/4);
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MATHEMATICA
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RealDigits[Pi/3 - Sqrt[3]/4, 10, 100][[1]]
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PROG
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(PARI) Pi/3 - sqrt(3)/4
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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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