A193720 Decimal expansion of Burnside curve length.

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Burnside Curve

Example

3.878554858741...

Mathematica

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]

Crossrefs

Cf. A193719 (area).

Sequence in context: A106043 A294833 A202478 * A011255 A342664 A101297

Adjacent sequences: A193717 A193718 A193719 * A193721 A193722 A193723

Keyword

nonn,cons

Author

Jean-François Alcover, Aug 03 2011

Extensions

Mathematica program simplified by Jean-François Alcover, Aug 26 2011

Status

approved