#osculatingcircle — Public Fediverse posts

Osculating Circles Revisited

Every squiggly line could be an image of the meandering trajectory of a particle. At each instant, the path has a direction and a curvature. Curvature can be represented by the circle that fits the curve best - the osculating circle. In a two-dimensional world, the osculating circles would lie flat in the same plane the tangent vectors are confined to. But in three dimensions also the "instantaneous plane" of the motion is changing. There are three vectors that describe the path in each […]

https://elkement.art/2026/07/29/osculating-circles-revisited/