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

  • Vito Lampret University of Ljubljana, 386 Slovenia.
Keywords: approximation, elementary, ellipse, estimate, Maclaurin series, mathematical validity, perimeter, simple


For the perimeter P (a, b) of an ellipse with the semi-axes ab ≥ 0 a sequence Qn(a, b) is constructed such that the relative error of the approximation P(a,b) ≈ Qn(a,b) satisfies the following inequalities

0 ≤ −(P(a,b)−Qn(a,b))/P(a,b) ≤ (1 −q2)n+1/(2n+1)2

≤ (1/(2n+1)2) e-q^2(n+1),  

true for n ∈ N and q = b/a ∈ [0,1].


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How to Cite
Lampret, V. (2019). The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series. CUBO, A Mathematical Journal, 21(2), 51-64.