# Affine pseudo-distance

The number $\rho = ( \overline{ {MM ^ {*} }}\; , \mathbf t )$, equal to the modulus of the vector product of the vectors $\overline{ {MM ^ {*} }}\;$ and $\mathbf t$, where $M ^ {*}$ is an arbitrary point in an equi-affine plane, $M$ is a point on a plane curve $\mathbf r = \mathbf r (s)$, $s$ is the affine parameter of the curve and $\mathbf t = d \mathbf r / ds$ is the tangent vector at the point $M$. This number $\rho$ is called the affine pseudo-distance from $M ^ {*}$ to $M$. If $M ^ {*}$ is held fixed, while $M$ is moved along the curve, the affine pseudo-distance from $M ^ {*}$ to $M$ will assume a stationary value if and only if $M ^ {*}$ lies on the affine normal of the curve at $M$. An affine pseudo-distance in an equi-affine space can be defined in a similar manner for a given hypersurface.