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Let C be a curve, let O be a fixed point (the pole), and let O^' be a second fixed point. Let P and P^' be points on a line through O meeting C at Q such that P^'Q=QP=QO^'. ...

Limacon of Pascal

Orthogonal circles are orthogonal curves, i.e., they cut one another at right angles. By the Pythagorean theorem, two circles of radii r_1 and r_2 whose centers are a ...

In general, there are two important types of curvature: extrinsic curvature and intrinsic curvature. The extrinsic curvature of curves in two- and three-space was the first ...

Bipolar coordinates are a two-dimensional system of coordinates. There are two commonly defined types of bipolar coordinates, the first of which is defined by x = ...

A set of n variables which fix a geometric object. If the coordinates are distances measured along perpendicular axes, they are known as Cartesian coordinates. The study of ...

The Radon-Nikodym theorem asserts that any absolutely continuous complex measure lambda with respect to some positive measure mu (which could be Lebesgue measure or Haar ...

A reference triangle is a triangle relative to which trilinear coordinates, exact trilinear coordinates, derived triangle, or other objects are defined in triangle geometry ...

Given a complex measure mu, there exists a positive measure denoted |mu| which measures the total variation of mu, also sometimes called simply "total variation." In ...

The azimuthal angle is an angle measured from the x-axis in the xy-plane in spherical coordinates, denoted theta in this work.