# 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.

## 10 Citations

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

- Mathematics
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In this paper, we present several bounds for the perimeter of an ellipse in terms of arithmetic, geometric, and harmonic means, which improve some known results. Mathematics subject classification…

Bounds for the perimeter of an ellipse

- Computer Science, MathematicsJ. Approx. Theory
- 2012

Several bounds for the perimeter of an ellipse are presented, which improve some well-known results.

The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series

- PhysicsCubo (Temuco)
- 2019

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 \(P(a,b)\approx Q_n(a,b)\)…

To Measure the Perimeter of an Ellipse Using Image Processing and Mathematical Reasoning

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A 2D continuous digital image a[x, y] is composed of m rows and n columns where x = {1, 2, ..., m} and y = {1, 2, ..., n}. RGB and CMYK are two main color spaces that indicate each pixel of a digital…

Convexity and concavity of the complete elliptic integrals with respect to Lehmer mean

- Mathematics
- 2015

In this paper, the authors present necessary and sufficient conditions for the complete elliptic integrals of the first and second kind to be convex or concave with respect to the Lehmer mean.

Very accurate approximations for the elliptic integrals of the second kind in terms of Stolarsky means

- Mathematics
- 2015

For $a,b>0$ with $a\neq b$, the Stolarsky means are defined by% \begin{equation*} S_{p,q}\left(a,b\right) =\left({\dfrac{q(a^{p}-b^{p})}{p(a^{q}-b^{q})}}% \right)…

Automated Image Analysis for Systematic and Quantitative Comparison of Protein Expression within Cell Populations

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It is shown that cell-to-cell ’spatial variability’ is a protein expression property, whose measurement is only possible from microscopy images, that allows the systematic detection of many classes of such variability, without the use of any prior knowledge about subcellular localization.

How beetles explode : new insights into the operation, structure, and materials of bombardier beetle (Brachinini) defensive glands

- Materials Science
- 2015

Bombardier beetles possess one of the most
remarkable defense mechanisms in nature, using explosions inside
their bodies to synthesize and eject a hot, noxious spray at
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How much faster does the best polynomial approximation converge than Legendre projection?

- Computer Science, MathematicsNumerische Mathematik
- 2021

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…

How fast does the best polynomial approximation converge than Legendre projection?

- Computer ScienceArXiv
- 2020

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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