Half Plane

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half plane [′haf ¦plān]

(mathematics)

The portion of a plane lying on one side of some line in the plane; in particular, all points of the complex plane either above or below the real axis.

Half Plane

in mathematics, the set of points of a plane that lie on one side of some line in the plane. The coordinates of points in a half plane satisfy the inequality Ax + By + C > 0, where A, B, and C are constants such that A and B are not simultaneously equal to zero. The line Ax + By + C = 0 is called the boundary of the half plane. If the boundary is included in the half plane, the half plane is said to be closed.

The complex plane z = x + iy contains an upper half plane y = Im z > 0, a lower half plane y = Im z < 0, a left half plane x = Re z < 0, a right half plane x = Re z > 0, and so on. The upper half plane of the complex z-plane is mapped conformally onto the circle ǀwǀ < 1 by the linear fractional function

where θ is an arbitrary real number and Im β > 0.

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No references found			Topics include non-archimedean analytical geometry, approaches to non-archimedean geometry, the p-adic upper half plane, Berkovich analytic spaces and non-archimedean potential theory on curves, and p-adic cohomology from theory to practice. p-adic geometry; lectures from the 2007 Arizona Winter School by SciTech Book News			half baluster half bat half bath half block half board half bond half brick half Cape house half carry half chronometer half cock half column half cycle half door half dovetail half figure half hatchet half header half house half landing Half Line Half Moon Bay Art and Pumpkin Festival Half Moon Bay State Beach Half Moon Pond State Park half nut Half Plane half principal half round half S-trap half section half set half slating Half Space half step half story half tap half term half thickness half tide half timber half time half tone half truss half volley half-adder half-adjust half-and-half half-and-half solder half-angle formulas half-arc angle half-bastion			Half Nekkid Thursday half nelson half nelsons half nelsons half note Half notes half nut Half O Scale Half Object Plus Protocol Half on Half Half Operational Capability Half or Triple Plus One Half Ounce half page Half Page Double Spread Half Page Double Spreads half past one half past one half past one half past one half past two half past two half past two half past two Half pay Half penny Half penny half pipe half pipe Half Pixel Motion Estimation Half Plane Half Position half pound Half Power Diameter Half price Half Price Books Half Price Jewellery half principal Half proof Half Rao-Wilton-Glisson Function Half Rate Half reaction equation balancing Half reaction equation balancing Half reaction equation balancing half relief half reliefs half rest half rhyme Half rhymes Half rhyming Half round Half round half S-trap Half seal Half seas over half section half section Half Securon half set

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