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A118289
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Decimal expansion of the arc length of the bifoliate.
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0
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6, 4, 7, 9, 9, 1, 1, 9, 5, 9, 8, 4, 6, 4, 1, 6, 5, 5, 9, 9, 4, 0, 2, 1, 3, 7, 1, 4, 1, 0, 1, 9, 3, 8, 3, 2, 9, 5, 4, 3, 7, 3, 3, 1, 4, 4, 3, 0, 6, 5, 6, 3, 8, 8, 4, 1, 4, 2, 6, 1, 9, 6, 7, 4, 8, 2, 6, 6, 2, 7, 8, 4, 0, 1, 1, 6, 8, 8, 2, 9, 5, 6, 4, 1, 1, 0, 2, 7, 6, 6, 9, 1, 9, 8, 8, 9, 1, 3, 3, 1, 0, 8, 8, 0, 9
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Eric Weisstein's World of Mathematics, Bifoliate
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EXAMPLE
| 6.4799119598464165599...
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MATHEMATICA
| f1[x_] := Sqrt[x + Sqrt[x^2 - x^4]]; f2[x_] := Sqrt[x - Sqrt[x^2 - x^4]]; g1[y_] = x /. Solve[y == f1[x], x][[4]]; g2[y_] = x /. Solve[y == f2[x], x][[4]]; x1 = 7/8; y1 = f1[x1]; y2 = f2[x1]; ni[f_, x_] := NIntegrate[f, x, WorkingPrecision -> 120]; i1 = ni[Sqrt[1 + f1'[x]^2], {x, 0, x1}]; i2 = ni[Sqrt[1 + f2'[x]^2], {x, 0, x1}]; i3 = ni[Sqrt[1 + g1'[y]^2], {y, 1, y1}]; i4 = ni[Sqrt[1 + g2'[y]^2], {y, y2, 1}]; Take[RealDigits[2(i1+i2+i3+i4)][[1]], 105] (* From Jean-François Alcover, Nov 25 2011 *)
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CROSSREFS
| Sequence in context: A011486 A153306 A092160 * A075495 A070652 A195487
Adjacent sequences: A118286 A118287 A118288 * A118290 A118291 A118292
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KEYWORD
| nonn,cons
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Apr 22, 2006
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