A359104 Decimal expansion of the area enclosed by Sylvester's Bicorn curve.

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

Offset

0,1

Comments

The Cartesian equation of Sylvester's Bicorn curve is y^2*(m^2-x^2) = (x^2+2*m*y-m^2)^2, here with parameter m=1. The area is proportional to the square m^2 of parameter m.

Corresponding arc length is given by A228764.

References

M. Protat, Des Olympiades à l'Agrégation, Encadrement du bicorne, Problème 66, pp. 142-145, Ellipses, Paris 1997.

Links

Table of n, a(n) for n=0..98.

Robert Ferréol, Bicorn, Mathcurve.

Eric Weisstein's World of Mathematics, Bicorn.

Wikipedia, Bicorn.

Index to sequences related to curves.

Formula

Equals (16*sqrt(3) - 27)*Pi/3.

Example

0.746455945439346463341461672758965758770535375107896820343...

Maple

evalf((16*sqrt(3) - 27)*Pi/3, 100);

Mathematica

RealDigits[(16*Sqrt[3] - 27)*Pi/3, 10, 120][[1]] (* Amiram Eldar, Dec 18 2022 *)

Crossrefs

Cf. A228764 (length).

Other area of curves: A019692 (deltoid), A197723 (cardioid), A122952 (nephroid), A180434 (Newton strophoid).

Sequence in context: A021138 A336763 A195366 * A185196 A347909 A085665

Adjacent sequences: A359101 A359102 A359103 * A359105 A359106 A359107

Keyword

nonn,cons

Author

Bernard Schott, Dec 18 2022

Status

approved