Perimeter determination of the eight-centered oval (Q2204970)

This is a slight variation of [C. R., Math., Acad. Sci. Paris 356, No. 11--12, 1195--1202 (2018; Zbl 1412.51006)] by the same authors, which is not listed in this paper's bibliography. It consists of (1) a history of approximations or computations of the exact value of the perimeter of an ellipse, in which Heron, Kepler, Euler, Maclaurin, Fagnano, Ivory, Peano, Ramanujan are mentioned; (2) ellipses and other ellipse-like ovals in architecture; (3) the work of F. R. Honey on the approximation of the ellipse by an eight-centered oval; (4) carried-out computations of the perimeter of the eight-centered oval, which show that ``the relative error between the two expressions [of the perimeter of the ellipse and that of the eight-centered oval] remains less than \(0.029\%\).''