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arXiv · 2403.04944

The area of H\"ugelsch\"affer curves via Taylor series

Maja Petrovic·Branko Malesevic
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Abstract

In this paper, we give new Taylor approximative formulae for the area of the egg-shaped parts of H\"ugelsch\"affer curves. Based on a parametrization of the H\"ugelsch\"affer curve, a formula for the area of the egg-shaped part of such a curve is derived via elliptic integrals of the first and second kind. Furthermore, new approximative formulae for calculating this area derived from standard and double Taylor approximations are given. A representation of the value $\frac{1}{\pi}$ was also obtained using an appropriate series.

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Maja Petrovic, Branko Malesevic. 2024-03-07. The area of H\"ugelsch\"affer curves via Taylor series. https://arxiv.org/abs/2403.04944

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