A193625 Decimal expansion of bicuspid curve area.

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

Offset

1,1

Links

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

Eric Weisstein's World of Mathematics, Bicuspid Curve.

Example

3.746606978...

Mathematica

f[x_, y_] = (x^2 - 1)*(x - 1)^2 + (y^2 - 1)^2; sy = Solve[f[x, y] == 0, y]; sx = Solve[f[x, y] == 0, x]; s = Solve[f[x, -x + 1/2] == 0, x] ; f1[x_] = y /. sy[[4, 1]]; f2[x_] = y /. sy[[2, 1]]; g1[y_] = x /. sx[[3, 1]]; g2[y_] = x /. sx[[4, 1]]; x2 = x /. s[[3]]; y2 = f1[x2]; x6 = x /. s[[4]]; y6 = f2[x6]; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120]; a1 = ni[f1[x] - 1, {x, x2, 1} ]; a2 = ni[x2 - g1[y], {y, 1, y2}]; a3 = ni[-g1[y], {y, 0, 1}]; a4 = ni[g2[y], {y, 0, y6}]; a5 = ni[1 - f2[x], {x, x6, 1}]; a6 = x6*(1 - y6); a = 2*(a1 + a2 + a3 + a4 + a5 + a6); Take[RealDigits[a][[1]], 105]

Crossrefs

Cf. A193626 (length).

Sequence in context: A094689 A019831 A199733 * A198886 A305202 A340013

Adjacent sequences: A193622 A193623 A193624 * A193626 A193627 A193628

Keyword

nonn,cons

Author

Jean-François Alcover, Aug 01 2011

Status

approved