Yet another mathematical model of eggs: two-parametric Brandt's shapes (Q6174561)

This is part of a ``series of short reviews in which the existing ``models'' [for eggs] are covered in some depth and where possible -- appropriately extended'' that the author have recently embarked upon (``an almost exhaustive list of such ``models'' can be found in \textit{W. Hortsch} [Alte und neue Eiformeln in der Geschichte der Mathematik. München: Selbstverlag Hortsch (1990)]''). The model analysed here was proposed in an obscure venue by \textit{G. Brandt} [The research of an equation of a shell formed by the two-focus curve, in: Sb. tr. VZPI: ``Stroitelstvo i arhitektura''. Moscow: VZBI. 76--86 (1973)]. It is a surface of revolution described by \[ z^2 + y^2 = \frac{3x(2a - x)((x+a)^2-c^2)}{4(x+a)^2}\quad x\in[0, 2a] \] in which \(a > \)c are real positive parameters