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

@article{Lampret2019ThePO,
title={The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series},
author={Vito Lampret},
journal={Cubo (Temuco)},
year={2019}
}
• V. Lampret
• Published 10 August 2019
• Mathematics
• Cubo (Temuco)
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 $$P(a,b)\approx Q_n(a,b)$$ satisfies the following inequalities $$0\le -\frac{P(a,b)-Q_n(a,b)}{P(a,b)}\le\frac{(1-q^2)^{n+1}}{(2n+1)^2}$$ $$\le \frac{1}{(2n+1)^2}\,e^{-q^2(n+1)},$$ true for $$n\in{\mathbb N}$$ and $$q=\frac{b}{a}\in[0,1]$$.
2 Citations

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