Sextactic point

In projective geometry, the Laguerre–Forsyth invariant is a cubic differential that is an invariant of a projective plane curve. It is named for Edmond Laguerre and Andrew Forsyth, the latter of whom analyzed the invariant in an influential book on ordinary differential equations.

Suppose that ${\displaystyle p:\mathbf {P} ^{1}\to \mathbf {P} ^{2}}$ is a three-times continuously differentiable immersion of the projective line into the projective plane, with homogeneous coordinates given by ${\displaystyle p(t)=(x_{1}(t),x_{2}(t),x_{3}(t))}$ then associated to p is the third-order ordinary differential equation

...
Wikipedia