info prev up next book cdrom email home

Osculating Curves


An osculating curve to $f(x)$ at $x_0$ is tangent at that point and has the same Curvature. It therefore satisfies


for $k=0$, 1, 2. The point of tangency is called a Tacnode. The simplest example of osculating curves are $x^2$ and $x^4$, which osculate at the point $x_0=0$.

See also Tacnode

© 1996-9 Eric W. Weisstein