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A circle of radius 1 (using this distance) is the von Neumann neighborhood of its centre. A circle of radius r for the Chebyshev distance ( L ∞ metric ) on a plane is also a square with side length 2 r parallel to the coordinate axes, so planar Chebyshev distance can be viewed as equivalent by rotation and scaling to planar taxicab distance.
The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. [1] Angles in polar notation are generally expressed in either degrees or radians (2 π rad being equal to 360°).
Illustration of a unit circle. The variable t is an angle measure. Animation of the act of unrolling the circumference of a unit circle, a circle with radius of 1. Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1]
In the cylindrical coordinate system, a z-coordinate with the same meaning as in Cartesian coordinates is added to the r and θ polar coordinates giving a triple (r, θ, z). [8] Spherical coordinates take this a step further by converting the pair of cylindrical coordinates ( r , z ) to polar coordinates ( ρ , φ ) giving a triple ( ρ , θ ...
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
Radius = zenith distance: zd [nm] = 60 ⋅ (90 - Ho) (aka co-altitude of Ho) As the circles used for navigation generally have a radius of thousands of miles, a segment a few tens of miles long closely approximates a straight line, as described in Sumner's original use of the method.
The relation between and are given by the following table, where the values for DRMS and 2DRMS (twice the distance root mean square) are specific to the Rayleigh distribution and are found numerically, while the CEP, R95 (95% radius) and R99.7 (99.7% radius) values are defined based on the 68–95–99.7 rule
A circle of radius r for the Chebyshev distance (L ∞ metric) on a plane is also a square with side length 2r parallel to the coordinate axes, so planar Chebyshev distance can be viewed as equivalent by rotation and scaling to planar taxicab distance.