# Inequalities for the perimeter of an ellipse

@article{Jameson2014InequalitiesFT, title={Inequalities for the perimeter of an ellipse}, author={G. J. O. Jameson}, journal={The Mathematical Gazette}, year={2014}, volume={98}, pages={227 - 234} }

The perimeter of the ellipse x 2/a 2 + y 2/b 2 = 1 is 4J (a, b), where J (a, b) is the ‘elliptic integral’ This integral is interesting in its own right, quite apart from its application to the ellipse. It is often considered together with the companion integral Of course, we may as well assume that a and b are non-negative.

## 9 Citations

Bounds of the perimeter of an ellipse using arithmetic, geometric and harmonic means

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For the perimeter \(P(a,b)\) of an ellipse with the semi-axes \(a\ge b\ge 0\) a sequence \(Q_n(a,b)\) is constructed such that the relative error of the approximation \(P(a,b)\approx Q_n(a,b)\)…

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How much faster does the best polynomial approximation converge than Legendre projection?

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We compare the convergence behavior of best polynomial approximations and Legendre and Chebyshev projections and derive optimal rates of convergence of Legendre projections for analytic and…

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