The Cartesian ovals (Q6114818)

Cartesian ovals, as constructed by Descartes in 1637, are a natural generalization of conics; they are irreducible quartic algebraic curves. The author relates these curves to the gardener's construction of ellipses, to the Minkowski product of two circles (where \(\mathbb R^2\) is identified with \(\mathbb C\)) and to the refraction of spherical waves by spherical surfaces.