The word "pole" is used prominently in a number of very different branches of mathematics. Perhaps the most important and widespread usage is to denote a singularity
of a complex function. In inversive geometry,
the inversion pole is related to inverse
points with respect to an inversion circle.
The term "pole" is also used to denote the degenerate points and
in spherical coordinates, corresponding
to the north pole and south
pole respectively. "All-poles method" is an alternate term for the
maximum entropy method used in deconvolution.
In triangle geometry, an orthopole is the point
of concurrence certain perpendiculars with respect to a triangle of a given line,
and a Simson line pole is similarly defined based
on the Simson line of a point with respect to a triangle.
In projective geometry, the perspector
is sometimes known as the perspective pole.