cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A363876 Decimal expansion of the geometric mean of the isoperimetric quotient of ellipses when expressed in terms of their eccentricity.

Original entry on oeis.org

9, 1, 6, 8, 1, 6, 9, 2, 3, 3, 8, 2, 1, 6, 8, 2, 4, 8, 1, 7, 5, 4, 6, 2, 5, 3, 8, 5, 7, 2, 3, 7, 0, 4, 0, 4, 5, 6, 7, 3, 5, 3, 2, 9, 4, 9, 9, 3, 7, 3, 6, 2, 4, 4, 3, 3, 7, 8, 4, 0, 1, 6, 6, 5, 1, 9, 8, 9, 0, 1, 3, 8, 4, 8, 1, 5, 9, 1, 0, 1, 0, 3, 4, 9, 0, 0, 0, 4
Offset: 0

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Author

Tian Vlasic, Jun 25 2023

Keywords

Comments

The isoperimetric quotient of a curve is defined as Q = (4*Pi*A)/p^2, where A and p are the area and the perimeter of that curve respectively.
The isoperimetric quotient of an ellipse depends only on its eccentricity e in accordance to the formula Q = (Pi^2*sqrt(1-e^2))/(4*E(e)^2), where E() is the complete elliptic integral of the second kind.

Examples

			0.916816923382168248...
		

Crossrefs

Programs

  • Mathematica
    First[RealDigits[Pi^2/2*Exp[-1 - 2*NIntegrate[Log[EllipticE[x^2]], {x, 0, 1}, WorkingPrecision -> 100]]]]

Formula

Equals ((Pi^2)/2) * exp(-1-2*Integral_{x=0..1} log(E(x)) dx).