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A201424
Decimal expansion of the piriform curve length.
0
7, 0, 4, 2, 4, 9, 4, 4, 6, 8, 1, 3, 6, 2, 8, 0, 6, 2, 2, 7, 7, 8, 0, 6, 5, 5, 7, 8, 5, 1, 7, 0, 7, 0, 1, 3, 4, 3, 7, 5, 3, 4, 3, 6, 4, 2, 5, 0, 6, 7, 7, 4, 8, 9, 6, 2, 2, 5, 2, 0, 2, 5, 9, 4, 2, 3, 3, 5, 6, 3, 9, 3, 4, 3, 1, 2, 7, 4, 0, 9, 2, 1, 9, 8, 2, 4, 3, 6, 9, 7, 0, 8, 6, 0, 5, 8, 6, 8, 4, 7, 0, 5, 7, 4, 0
OFFSET
1,1
COMMENTS
The piriform curve Cartesian equation used is a^4*y^2 = b^2*x^3*(2*a-x) with a=b=1, i.e., y^2 = x^3*(2-x).
LINKS
Eric Weisstein's World of Mathematics, Piriform
EXAMPLE
7.042494468...
MATHEMATICA
f[x_] := Sqrt[2*x^3 - x^4]; g[y_] = x /. Solve[f[x] == y, x][[4]]; i1 = NIntegrate[ Sqrt[1 + f'[x]^2], {x, 0, 7/4}, WorkingPrecision -> 120]; i2 = NIntegrate[ Sqrt[1 + g'[y]^2], {y, 0, f[7/4]}, WorkingPrecision -> 120]; Take[ RealDigits[2(i1+i2)][[1]], 105]
CROSSREFS
Sequence in context: A245637 A286193 A021146 * A070513 A065463 A319739
KEYWORD
cons,easy,nonn
AUTHOR
STATUS
approved