A193721 Decimal expansion of Dumbbell curve length.

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

Offset

1,1

Links

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

Eric Weisstein's World of Mathematics, Dumbbell Curve

Example

5.54100277...

Mathematica

f[x_, y_] = y^2 - x^4 (1 - x^2); f[x_] = Sqrt[x^4 - x^6]; x0 = 9/10; y0 = f[x0]; g[y_] = x /. Solve[f[x, y] == 0, x][[2]]; i1 = NIntegrate[ Sqrt[1 + f'[x]^2], {x, 0, x0}, WorkingPrecision -> 120]; i2 = NIntegrate[ Sqrt[1 + g'[y]^2], {y, 0, y0}, WorkingPrecision -> 120]; Take[ RealDigits[4(i1+i2)][[1]], 105]

Crossrefs

Sequence in context: A158274 A202695 A110986 * A019927 A332506 A019805

Adjacent sequences: A193718 A193719 A193720 * A193722 A193723 A193724

Keyword

nonn,cons

Author

Jean-François Alcover, Aug 03 2011

Status

approved