cp's OEIS Frontend

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

%I A359104 #32 Feb 16 2025 08:34:04
%S A359104 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 A359104 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 A359104 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 A359104 Decimal expansion of the area enclosed by Sylvester's Bicorn curve.
%C A359104 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 A359104 Corresponding arc length is given by A228764.
%D A359104 M. Protat, Des Olympiades à l'Agrégation, Encadrement du bicorne, Problème 66, pp. 142-145, Ellipses, Paris 1997.
%H A359104 Robert Ferréol, <a href="https://mathcurve.com/courbes2d.gb/bicorne/bicorne.shtml">Bicorn</a>, Mathcurve.
%H A359104 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Bicorn.html">Bicorn</a>.
%H A359104 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bicorn">Bicorn</a>.
%H A359104 <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Cu">Index to sequences related to curves</a>.
%F A359104 Equals (16*sqrt(3) - 27)*Pi/3.
%e A359104 0.746455945439346463341461672758965758770535375107896820343...
%p A359104 evalf((16*sqrt(3) - 27)*Pi/3, 100);
%t A359104 RealDigits[(16*Sqrt[3] - 27)*Pi/3, 10, 120][[1]] (* _Amiram Eldar_, Dec 18 2022 *)
%Y A359104 Cf. A228764 (length).
%Y A359104 Other area of curves: A019692 (deltoid), A197723 (cardioid), A122952 (nephroid), A180434 (Newton strophoid).
%K A359104 nonn,cons
%O A359104 0,1
%A A359104 _Bernard Schott_, Dec 18 2022