Half-plane
From Encyclopedia of Mathematics
The set of points in a plane situated to one side of a given straight line in that plane. The coordinates of the points of a half-plane satisfy an inequality , where
are certain constants such that
and
do not vanish simultaneously. If the straight line
itself (the boundary of the half-plane) belongs to the half-plane, the latter is said to be closed. Special half-planes on the complex plane
are the upper half-plane
, the lower half-plane
, the left half-plane
, the right half-plane
, etc. The upper half-plane of the complex
-plane can be mapped conformally (cf. Conformal mapping) onto the disc
by the Möbius transformation
![]() |
where is an arbitrary real number and
.
How to Cite This Entry:
Half-plane. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Half-plane&oldid=47162
Half-plane. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Half-plane&oldid=47162
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article