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A101801
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Decimal expansion of the area of the ampersand curve.
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1
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1, 0, 6, 6, 5, 5, 5, 0, 9, 5, 4, 5, 7, 3, 2, 7, 4, 6, 3, 7, 5, 3, 9, 1, 3, 9, 1, 3, 3, 6, 9, 1, 1, 9, 1, 3, 5, 7, 5, 5, 3, 9, 2, 3, 3, 9, 8, 4, 7, 7, 4, 9, 8, 9, 0, 2, 3, 7, 1, 7, 7, 0, 4, 4, 6, 4, 0, 4, 9, 8, 9, 3, 5, 1, 5, 1, 7, 9, 3, 2, 4, 8, 3, 8, 1, 1, 8, 0, 2, 1, 8, 7, 7, 1, 9, 9, 7, 2, 5, 7, 3, 0, 6, 6, 3
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OFFSET
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1,3
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LINKS
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EXAMPLE
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1.06655509...
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MATHEMATICA
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eq = (y^2 - x^2)(x - 1)(2x - 3) == 4 (x^2 + y^2 - 2x)^2 ;
sy = Solve[eq, y]; f1[x_] = y /. sy[[2]]; f2[x_] = y /. sy[[4]]; x1 = x /. FindRoot[f1'[x] == 1, {x, 31/21}, WorkingPrecision -> 120 ]; y1 = y /. Solve[eq /. x -> x1][[3]]; y2 = y /. Solve[eq /. x -> x1][[4]]; sx = Solve[eq, x]; g1[y_] = x /. sx[[1]]; g2[y_] = Simplify[x /. sx[[4]], y1 < y < y2]; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120]; i1 = ni[Simplify[-g1[y], 0 < y < Sqrt[3]/2] , {y, 0, Sqrt[3]/2}]; i2 = ni[f2[x] - f1[x], {x, 0, 1}]; i3 = ni[f2[x] - f1[x], {x, 1, x1}]; i4 = ni[g2[y] - x1 , {y, y1, y2}]; Take[RealDigits[2 (i1 + i2 + i3 + i4)][[1]], 105]
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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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