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A193720 Decimal expansion of Burnside curve length. 1

%I #17 Jul 03 2015 05:19:28

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

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

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

%N Decimal expansion of Burnside curve length.

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

%e 3.878554858741...

%t f[x_, y_] = y^2 - x (x^4 - 1); f[x_] = Sqrt[-x + x^5]; x1 = -5/6; y1 = f[x1]; x2 = -1/4; y2 = f[x2]; eq = Eliminate[f[g[y], y] == 0 && D[f[g[y], y], y] == 0, g[y]]; dg1[y_] = g'[y] /. Solve[eq, g'[y]][[3]]; dg2[y_] = g'[y] /. Solve[eq, g'[y]][[1]]; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120]; i1 = ni[Sqrt[1 + dg1[y]^2], {y, 0, y1}]; i2 = ni[Sqrt[1 + f'[x]^2], {x, x1, x2}]; i3 = ni[Sqrt[1 + dg2[y]^2], {y, 0, y2}]; Take[RealDigits[2(i1+i2+i3)][[1]], 105]

%Y Cf. A193719 (area).

%K nonn,cons

%O 1,1

%A _Jean-Fran├žois Alcover_, Aug 03 2011

%E Mathematica program simplified by _Jean-Fran├žois Alcover_, Aug 26 2011

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Last modified February 29 02:52 EST 2024. Contains 370401 sequences. (Running on oeis4.)