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Arc measurement, [1] sometimes called degree measurement [2] (German: Gradmessung), [3] is the astrogeodetic technique of determining the radius of Earth and, by extension, its circumference.
Extensions to the above notation allow the GEOREF system to be used to designate an area around a reference point. This is achieved by adding an area designation to a base GEOREF co-ordinate. The area designation can be the letter S, to specify the sides of a rectangle (separated by the letter X); or the letter R, to specify the radius of a circle.
View from the Swabian Jura to the Alps. Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length.. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude.
The equivalent latitude from the area is given as: = where A is the area enclosed to the South (A = 0 corresponds to the equivalent South Pole) and R is the radius of the Earth. This method generates a mapping that is as continuous as the data allows as opposed to binning which produces a coarse-grained mapping.
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
Formulas for the Web Mercator are fundamentally the same as for the standard spherical Mercator, but before applying zoom, the "world coordinates" are adjusted such that the upper left corner is (0, 0) and the lower right corner is ( , ): [7] = ⌊ (+) ⌋ = ⌊ ( [ (+)]) ⌋ where is the longitude in radians and is geodetic latitude in radians.
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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 ).