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A193721 Decimal expansion of Dumbbell curve length. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified February 23 02:31 EST 2024. Contains 370265 sequences. (Running on oeis4.)