In
differential geometry, an
osculating curve is a
plane curve from a given family that has the highest possible order of
contact with another curve. That is, if
F is a family of
smooth curves,
C is a smooth curve (not in general belonging to
F), and
p is a point on
C, then an osculating curve from
F at
p is a curve from
F that passes through
p and has as many of its
derivatives at
p equal to the derivatives of
C as possible.