quadrant

The $x$- and $y$-axes the $xy$-plane in four right-angle domains which are called the quadrants of the plane.  They are numbered going round the origin in anticlockwise direction so that

$$\{(x,y)\mid x>0,y>0\}$$

is the first quadrant,

the second quadrant, and so on.

Naturally, one can speak of the quadrants of the complex plane, too.

The lines $y=\pm x$ have as their slope angles $\pm {45}^{\circ }$, thus halving the quadrant angles; they are called the quadrant bisectors.  Cf. angle bisector as locus.

Title	quadrant
Canonical name	Quadrant
Date of creation	2014-12-16 22:42:51
Last modified on	2014-12-16 22:42:51
Owner	Mathprof (13753)
Last modified by	pahio (2872)
Numerical id	14
Author	Mathprof (2872)
Entry type	Definition
Classification	msc 51N20
Synonym	quarter-plane
Related topic	RightAngle
Related topic	ConvexAngle
Related topic	Octant
Defines	1st quadrant
Defines	2nd quadrant
Defines	3rd quadrant
Defines	4th quadrant