Upper half-plane

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In mathematics, the upper half-plane, ⁠${\displaystyle {\mathcal {H}},}$⁠ is the set of points ⁠${\displaystyle (x,y)}$⁠ in the Cartesian plane with ⁠${\displaystyle y>0.}$⁠ The lower half-plane is the set of points ⁠${\displaystyle (x,y)}$⁠ with ⁠${\displaystyle y<0}$⁠ instead. Arbitrary oriented half-planes can be obtained via a planar rotation. Half-planes are an example of two-dimensional half-space. A half-plane can be split in two quadrants.