• DOI:10.4067/s0719-06462019000200051
• Corpus ID: 208629053

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 \(q=\frac{b}{a}\in[0,1]\).