A201424 Decimal expansion of the piriform curve length.

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

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

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

Adjacent sequences: A201421 A201422 A201423 * A201425 A201426 A201427

Keyword

cons,easy,nonn

Author

Jean-François Alcover, Dec 01 2011

Status

approved