Mathematical principles underlying
the method
In mathematics, a curvature is
described by means of
hypothetical circles.
The
curvature at a specific point (x 0) is
described by selecting a circle
that is optimally adapted to
the configuration of the curve at
that point (x 0).
The
smaller the curvature, the larger
the hypothetical circle.
The curvature dimension at a point
(x 0) is specified by the
reciprocal value of the radius of the corresponding
hypothetical circle:
Before analytical methods can be
used to investigate
root canal curvature,
a
mathematical model of the configuration
of the curve has to be produced for
the inner
(small) curve and the outer
(large) curve.
The actual configuration
of the canal wall is described by
specifying x,y
coordinates of selected measuring
points.
Using this point
sequence, an equalising function
describing the configuration
in mathematical terms can be
determined.
The quality
of the adaptation of the
equalising function to the point
sequence is described by the
so-called degree of accuracy
(correlation coefficient).
The
less this dimension deviates
from 1, the better the adaptation.
Use of the equalising function
adapted to the configuration
of the long axis of the canal
permits exact determination
of the curvature for each point x
and for the point of
maximum curvature, as well as the
mean curvature of the
measured canal section. In the
formula used, the configuration
ascertained for the curve is
designated y (x ), and the
pertinent curvature function k (x ).
The distance of the point of
maximum curvature from
the apical foramen can also be calculated by means
of the