# 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.

**How to Cite This Entry:**

Affine pseudo-distance.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Affine_pseudo-distance&oldid=45048