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

Author

Bernard Schott, Dec 18 2022

Keywords

• nonn
• cons

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.

Examples

			0.746455945439346463341461672758965758770535375107896820343...
		

References

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

Links

• Robert Ferréol, Bicorn, Mathcurve.
• Eric Weisstein's World of Mathematics, Bicorn.
• Wikipedia, Bicorn.
• Index to sequences related to curves.

Crossrefs

Cf. A228764 (length).

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

Programs

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 *)

Formula

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