View source for Affine pseudo-distance

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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|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.