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

dc.creatorLampret, Vito
dc.date2019-08-10
dc.identifierhttp://revistas.ufro.cl/ojs/index.php/cubo/article/view/2158
dc.identifier10.4067/S0719-06462019000200051
dc.descriptionFor 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 \(q=\frac{b}{a}\in[0,1]\).en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad de La Frontera. Temuco, Chile.en-US
dc.relationhttp://revistas.ufro.cl/ojs/index.php/cubo/article/view/2158/1889
dc.rightsCopyright (c) 2019 CUBO, A Mathematical Journalen-US
dc.sourceCUBO, A Mathematical Journal; Vol. 21 No. 2 (2019); 51-64en-US
dc.sourceCUBO, A Mathematical Journal; Vol. 21 Núm. 2 (2019); 51-64es-ES
dc.source0719-0646
dc.source0716-7776
dc.subjectapproximationen-US
dc.subjectelementaryen-US
dc.subjectellipseen-US
dc.subjectestimateen-US
dc.subjectMaclaurin seriesen-US
dc.subjectmathematical validityen-US
dc.subjectperimeteren-US
dc.subjectsimpleen-US
dc.titleThe perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s seriesen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion


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