cp's OEIS Frontend

A259830 Decimal expansion of the length of the "double egg" curve (length of one egg with diameter a = 1).

%I A259830 #10 Jul 09 2015 04:04:29
%S A259830 2,7,6,0,3,4,5,9,9,6,3,0,0,9,4,6,3,4,7,5,3,1,0,9,4,2,5,4,8,8,0,4,0,5,
%T A259830 8,2,4,2,0,1,6,2,7,7,3,0,9,4,7,1,7,6,4,2,7,0,2,0,5,7,0,6,7,0,2,6,0,0,
%U A259830 5,5,1,2,2,6,5,4,9,1,0,7,5,3,0,2,8,4,5,8,3,6,4,7,9,8,4,8,7,3,4,6,7,1,5
%N A259830 Decimal expansion of the length of the "double egg" curve (length of one egg with diameter a = 1).
%C A259830 Essentially the same as A196530. - _R. J. Mathar_, Jul 09 2015
%H A259830 Robert Ferréol (MathCurve), <a href="http://www.mathcurve.com/courbes2d/oeufdouble/oeufdouble.shtml">Oeuf double, Double egg, Doppeleikurve</a> [in French]
%H A259830 Jürgen Köller (Mathematische Basteleien), <a href="http://www.mathematische-basteleien.de/eggcurves.htm">Egg Curves and Ovals</a>
%F A259830 Polar equation: r(t) = a*cos(t)^2.
%F A259830 Cartesian equation: (x^2+y^2)^3 = a^2*x^4.
%F A259830 Area of one egg: A(a) = 3*Pi*a^2/16.
%F A259830 Length of one egg: L(a) = (a/3)*(6 + sqrt(3)*log(2 + sqrt(3))).
%e A259830 2.76034599630094634753109425488040582420162773094717642702057067026...
%t A259830 L[a_] := (a/3)*(6 + Sqrt[3]*Log[2 + Sqrt[3]]); RealDigits[L[1], 10, 103] // First
%o A259830 (PARI) (6 + sqrt(3)*log(2 + sqrt(3)))/3 \\ _Michel Marcus_, Jul 06 2015
%K A259830 nonn,cons,easy
%O A259830 1,1
%A A259830 _Jean-François Alcover_, Jul 06 2015