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The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = ...

A polar representation of a complex measure mu is analogous to the polar representation of a complex number as z=re^(itheta), where r=|z|, dmu=e^(itheta)d|mu|. (1) The analog ...

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 Radon transform is an integral transform whose inverse is used to reconstruct images from medical CT scans. A technique for using Radon transforms to reconstruct a map of ...

Reciprocation is an incidence-preserving transformation in which points are transformed into their polars. A projective geometry-like duality principle holds for ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

Fok (1946) and Hazewinkel (1988, p. 65) call v(z) = 1/2sqrt(pi)Ai(z) (1) w_1(z) = 2e^(ipi/6)v(omegaz) (2) w_2(z) = 2e^(-ipi/6)v(omega^(-1)z), (3) where Ai(z) is an Airy ...

The atom-spiral, also known as the atomic spiral, is the curve with polar equation r=theta/(theta-a) for a real parameter a (van Maldeghem 2002). When theta is allows to vary ...

A map projection on which the azimuths of all points are shown correctly with respect to the center (Snyder 1987, p. 4). A plane tangent to one of the Earth's poles is the ...

A curve whose name means skull-like. It is given by the polar equation r=asint+bsqrt(1-pcos^2t)+csqrt(1-qcos^2t), where a,b,c>0, a<b+c, 0<p<1, 0<q<1, and p!=q. The top of the ...