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 A228764 Decimal expansion of the arc length of Sylvester's Bicorn curve. 1
 5, 0, 5, 6, 5, 3, 0, 0, 3, 2, 1, 2, 1, 2, 4, 4, 9, 7, 3, 2, 7, 0, 1, 6, 4, 8, 9, 6, 6, 6, 0, 4, 7, 4, 4, 6, 8, 7, 8, 5, 9, 0, 1, 0, 6, 5, 6, 5, 4, 3, 7, 5, 4, 9, 2, 0, 1, 3, 7, 4, 5, 8, 0, 2, 9, 8, 6, 5, 3, 3, 5, 7, 6, 9, 0, 4, 0, 7, 5, 4, 6, 0, 4, 3, 8, 4, 8, 9, 3, 9, 1, 4, 3, 6, 0, 2, 8, 4, 7, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Cartesian equation used here is y^2*(t^2-x^2) = (x^2+2*t*y-t^2)^2, with t=1. The arc length (perimeter) is proportional to the parameter t. LINKS Table of n, a(n) for n=1..100. Eric Weisstein, Bicorn (MathWorld) Wikipedia, Bicorn EXAMPLE 5.056530032121244973270164896660474468785901065654375492013745802986533576904... MATHEMATICA digits = 100; y1[x_] := (1 - x^2)/(2 - Sqrt[1 - x^2]); y2[x_] := (1 - x^2)/(2 + Sqrt[1 - x^2]); i1 = NIntegrate[Sqrt[1 + y1'[x]^2], {x, -1, 1}, WorkingPrecision -> digits+5]; i2 = NIntegrate[Sqrt[1 + y2'[x]^2], {x, -1, 1}, WorkingPrecision -> digits+5]; RealDigits[i1 + i2][[1]][[1 ;; digits]] CROSSREFS Sequence in context: A055510 A200397 A265302 * A200631 A201939 A256192 Adjacent sequences: A228761 A228762 A228763 * A228765 A228766 A228767 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Sep 03 2013 STATUS approved

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Last modified April 23 19:56 EDT 2024. Contains 371916 sequences. (Running on oeis4.)