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A228764 Decimal expansion of the arc length of Sylvester's Bicorn curve. 0

%I

%S 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,

%T 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,

%U 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

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

%C 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.

%H Eric Weisstein, <a href="http://mathworld.wolfram.com/Bicorn.html">Bicorn</a> (MathWorld)

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bicorn">Bicorn</a>

%e 5.056530032121244973270164896660474468785901065654375492013745802986533576904...

%t 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]]

%K nonn,cons

%O 1,1

%A _Jean-Fran├žois Alcover_, Sep 03 2013

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Last modified June 19 17:25 EDT 2021. Contains 345144 sequences. (Running on oeis4.)