Filipe Bellio da Nobrega

The Tait-Kneser theorem is a well known result of differential geometry which states that the osculating circles of a plane curve with monotonic curvature and no inflection points are disjoint and nested. Therefore, an arc with no vertex gives rise to an interesting foliation of the region of the plane delimited by its largest and smallest osculating circle. In this talk, we will investigate the analogous result for osculating conics. It is already known that the osculating conics of a curve with no sextactic or inflection points are also disjoint and nested. However, we will show that the relative position of two such conics is actually more restricted than that, they are in some sense “convexly nested”.