OFFSET
1,1
COMMENTS
Essentially the same as A196530. - R. J. Mathar, Jul 09 2015
LINKS
Robert Ferréol (MathCurve), Oeuf double, Double egg, Doppeleikurve [in French]
Jürgen Köller (Mathematische Basteleien), Egg Curves and Ovals
FORMULA
Polar equation: r(t) = a*cos(t)^2.
Cartesian equation: (x^2+y^2)^3 = a^2*x^4.
Area of one egg: A(a) = 3*Pi*a^2/16.
Length of one egg: L(a) = (a/3)*(6 + sqrt(3)*log(2 + sqrt(3))).
EXAMPLE
2.76034599630094634753109425488040582420162773094717642702057067026...
MATHEMATICA
L[a_] := (a/3)*(6 + Sqrt[3]*Log[2 + Sqrt[3]]); RealDigits[L[1], 10, 103] // First
PROG
(PARI) (6 + sqrt(3)*log(2 + sqrt(3)))/3 \\ Michel Marcus, Jul 06 2015
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jul 06 2015
STATUS
approved