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 A193626 Decimal expansion of bicuspid curve length. 1

%I

%S 9,8,6,1,7,7,2,9,4,2,3,8,3,6,7,0,1,5,8,9,9,2,3,7,0,0,3,9,6,7,9,8,4,3,

%T 8,8,8,6,2,4,0,1,5,9,0,9,9,9,4,3,2,5,8,5,6,2,3,2,4,4,7,9,2,7,1,1,5,9,

%U 2,7,6,0,9,8,1,0,6,7,5,8,8,1,5,6,5,9,4,0,8,8,5,2,0,8,4,0,2,4,2,8,0,4,8,8,3

%N Decimal expansion of bicuspid curve length.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BicuspidCurve.html">BicuspidCurve</a>.

%e 9.861772942...

%t f[x_, y_] = (x^2 - 1)*(x - 1)^2 + (y^2 - 1)^2; sy = Solve[f[x, y] == 0, y]; sx = Solve[f[x, y] == 0, x]; s = Solve[f[x, -x + 1/2] == 0, x] ; f1[x_] = y /. sy[[4, 1]]; f2[x_] = y /. sy[[2, 1]]; g1[y_] = x /. sx[[3, 1]]; g2[y_] = x /. sx[[4, 1]]; x2 = x /. s[[3]]; y2 = f1[x2]; x6 = x /. s[[4]]; y6 = f2[x6]; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120]; ds1 = Sqrt[1 + f1'[x]^2] // Simplify; p1 = ni[ds1, {x, x2, 1} ] ; ds2 = Sqrt[1 + g1'[y]^2]; p2 = ni[ds2, {y, 0, y2}] ; ds3 = Sqrt[1 + g2'[y]^2]; p3 = ni[ds3, {y, 0, y6}] ; ds4 = Sqrt[1 + f2'[x]^2] // Simplify; p4 = ni[ds4, {x, x6, 1}] ; p = 2*(p1 + p2 + p3 + p4) ; Take[RealDigits[p][[1]], 105]

%Y Cf. A193625 (area)

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Aug 01 2011

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Last modified November 30 13:47 EST 2021. Contains 349420 sequences. (Running on oeis4.)