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In blue, the point (4, 210°). In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ...
The p-th polar of a C for a natural number p is defined as Δ Qpf (x, y, z) = 0. This is a curve of degree n − p. When p is n −1 the p -th polar is a line called the polar line of C with respect to Q. Similarly, when p is n −2 the curve is called the polar conic of C. Using Taylor series in several variables and exploiting homogeneity, f ...
Pole and polar. The polar line q to a point Q with respect to a circle of radius r centered on the point O. The point P is the inversion point of Q; the polar is the line through P that is perpendicular to the line containing O, P and Q. In geometry, a pole and polar are respectively a point and a line that have a unique reciprocal relationship ...
Cylindrical coordinate system. A cylindrical coordinate system with origin O, polar axis A, and longitudinal axis L. The dot is the point with radial distance ρ = 4, angular coordinate φ = 130°, and height z = 4. A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a ...
As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range of 180°, running from 0° to 180°, and does not pose any problem when calculated from an arccosine, but beware for an arctangent. If, in the alternative definition, θ is chosen to run from − ...
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same orbit, but certain schemes, each consisting of a set of six parameters, are commonly used in ...
Polarization identity. In linear algebra, a branch of mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space. If a norm arises from an inner product then the polarization identity can be used to express this inner product entirely in ...