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Points in the polar coordinate system with pole O and polar axis L. In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3, 60°). In blue, the point (4, 210°). In mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two coordinates. These are
Once the radius is fixed, the three coordinates (r, θ, φ), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane passing through the origin and perpendicular to the polar axis (where the polar angle is a right angle ) is called the reference plane (sometimes fundamental plane ).
This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.
In the case that the side c has length π /2 on the unit sphere the equations governing the remaining sides and angles may be obtained by applying the rules for the right spherical triangle of the previous section to the polar triangle A'B'C' with sides a', b', c' such that A' = π − a, a' = π − A etc.
The reference point (analogous to the origin of a Cartesian system) is called the pole, and the ray from the pole in the reference direction is the polar axis. The distance from the pole is called the radial coordinate or radius, and the angle is called the angular coordinate, or polar angle.
Like the UTM coordinate system, the UPS coordinate system uses a metric-based cartesian grid laid out on a conformally projected surface. UPS covers the Earth's polar regions, specifically the areas north of 84°N and south of 80°S, which are not covered by the UTM grids, plus an additional 30 minutes of latitude extending into UTM grid to ...
The area of the shape is proportional to the number of turns through which the measuring wheel rotates. The polar planimeter is restricted by design to measuring areas within limits determined by its size and geometry. However, the linear type has no restriction in one dimension, because it can roll.
Two-center bipolar coordinates. In mathematics, two-center bipolar coordinates is a coordinate system based on two coordinates which give distances from two fixed centers and . [1] This system is very useful in some scientific applications (e.g. calculating the electric field of a dipole on a plane). [2] [3]