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The word residue is used in a number of different contexts in mathematics. Two of the most common uses are the complex residue of a pole, and the remainder of a congruence. ...

The point at which the three lines connecting the vertices of two perspective triangles concur, sometimes also called the perspective center, homology center, or pole. In the ...

Two points are antipodal (i.e., each is the antipode of the other) if they are diametrically opposite. Examples include endpoints of a line segment, or poles of a sphere. ...

The azimuthal coordinate on the surface of a sphere (theta in spherical coordinates) or on a spheroid (in prolate or oblate spheroidal coordinates). Longitude is defined such ...

Complex Analysis

The triangle bounded by the polars of the vertices of a triangle DeltaABC with respect to a conic is called its polar triangle. The following table summarizes polar triangles ...

The latitude of a point on a sphere is the elevation of the point from the plane of the equator. The latitude delta is related to the colatitude (the polar angle in spherical ...

Cauchy's integral formula states that f(z_0)=1/(2pii)∮_gamma(f(z)dz)/(z-z_0), (1) where the integral is a contour integral along the contour gamma enclosing the point z_0. It ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

The Klein-Beltrami model of hyperbolic geometry consists of an open disk in the Euclidean plane whose open chords correspond to hyperbolic lines. Two lines l and m are then ...