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The pole of coordinates is the origin in polar coordinates.

A pole is the centre of an inversion.

The pole of the straight line $p$ with respect to a conic is the point $P$ such that the line $p$ is the polar of the point $P$ with respect to the conic.


For poles of (analytic) functions see Pole (of a function). Sometimes the word "pole" is used for the point $(0,0,1)$ (North pole) or $(0,0,-1)$ (South pole) of the unit sphere in $\mathbf R^3$, with centre at the origin.


[a1] M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French)
[a2] H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)
How to Cite This Entry:
Pole. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article