half-plane
Noun
Meaning
half-plane (plural half-planes)
(mathematics) Either half of an infinite plane (divided by a straight line)
Examples
Roughly speaking, continued fraction convergents can be taken to be Mobius transformations acting on the (hyperbolic) upper half-plane ; this is what leads to the fractal self-symmetry.
It is thus possible to ignore the flow in the lower half-plane where y < 0 and to focus on the flow in the upper half-plane.
Littlewood showed that if the sequence (γ n ) contains the imaginary parts of all zeros in the upper half-plane in ascending order, then : The critical line theorem asserts that a positive percentage of the nontrivial zeros lies on the critical line.
See also * Schwarz–Christoffel mapping – a conformal transformation of the upper half-plane onto the interior of a simple polygon.
The action of the modular group on the Poincaré half-plane is also wandering.
The circles in the upper half-plane thus flow clockwise, those in the lower half-plane flow anticlockwise.