A359104 - OEIS

%I #32 Feb 16 2025 08:34:04

%S 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,

%T 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,

%U 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

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

%C 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.

%C Corresponding arc length is given by A228764.

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

%H Robert Ferréol, <a href="https://mathcurve.com/courbes2d.gb/bicorne/bicorne.shtml">Bicorn</a>, Mathcurve.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Bicorn.html">Bicorn</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bicorn">Bicorn</a>.

%H <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Cu">Index to sequences related to curves</a>.

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

%e 0.746455945439346463341461672758965758770535375107896820343...

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

%t RealDigits[(16*Sqrt[3] - 27)*Pi/3, 10, 120][[1]] (* _Amiram Eldar_, Dec 18 2022 *)

%Y Cf. A228764 (length).

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

%K nonn,cons

%O 0,1

%A _Bernard Schott_, Dec 18 2022