In
differential geometry of curves, the
osculating circle of a sufficiently smooth plane
curve at a given point
p on the curve has been traditionally defined as the circle passing through
p and a pair of additional points on the curve
infinitesimally close to
p. Its center lies on the inner
normal line, and its
curvature is the same as that of the given curve at that point. This circle, which is the one among all
tangent circles at the given point that approaches the curve most tightly, was named
circulus osculans (Latin for "kissing circle") by
Leibniz.