A228764 Decimal expansion of the arc length of Sylvester's Bicorn curve.

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

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