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

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, 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, 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

Offset

1,1

Comments

Essentially the same as A196530. - R. J. Mathar, Jul 09 2015

Links

Table of n, a(n) for n=1..103.

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

Sequence in context: A051757 A193746 A070524 * A259235 A371801 A264692

Adjacent sequences: A259827 A259828 A259829 * A259831 A259832 A259833

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 06 2015

Status

approved