cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Bernard Schott, Dec 18 2022

Keywords

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

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.
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