Difference between revisions of "Pole"
From Encyclopedia of Mathematics
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The pole of coordinates is the origin in [[Polar coordinates|polar coordinates]]. | The pole of coordinates is the origin in [[Polar coordinates|polar coordinates]]. | ||
A pole is the centre of an [[Inversion|inversion]]. | A pole is the centre of an [[Inversion|inversion]]. | ||
| − | The pole of the straight line | + | The pole of the straight line $p$ with respect to a [[Conic|conic]] is the point $P$ such that the line $p$ is the [[Polar|polar]] of the point $P$ with respect to the conic. |
====Comments==== | ====Comments==== | ||
| − | For poles of (analytic) functions see [[Pole (of a function)|Pole (of a function)]]. Sometimes the word "pole" is used for the point | + | For poles of (analytic) functions see [[Pole (of a function)|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. |
====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Berger, "Geometry" , '''1–2''' , Springer (1987) (Translated from French)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Berger, "Geometry" , '''1–2''' , Springer (1987) (Translated from French)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)</TD></TR></table> | ||
Latest revision as of 19:31, 28 April 2014
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.
Comments
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.
References
| [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: http://encyclopediaofmath.org/index.php?title=Pole&oldid=12562
Pole. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pole&oldid=12562
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article