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Geographic Distance
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. This distance is an element in solving the second (inverse) geodetic problem. Introduction Calculating the distance between geographical coordinates is based on some level of abstraction; it does not provide an ''exact'' distance, which is unattainable if one attempted to account for every irregularity in the surface of the Earth. Common abstractions for the surface between two geographic points are: *Flat surface; *Spherical surface; *Ellipsoidal surface. All abstractions above ignore changes in elevation. Calculation of distances which account for changes in elevation relative to the idealized surface are not discussed in this article. Classification of Formulae based on Approximation * Tunnel-dista ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roßberg Alpen 1 (869 m), a mountain in the Swabian Jura, Baden-Württemberg, Germany
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Roßberg is a German name for a hill or mountain and may refer to: * Roßberg (Black Forest) (1,124.7 m), mountain in the Black Forest, Baden-Württemberg, Germany * Roßberg (Haardt) (637 m), third highest mountain in the Palatine Forest, Rhineland-Palatinate, Germany * Roßberg (Swabian Jura) The Roßberg is a mountain in Baden-Württemberg, Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its six ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delta (letter)
Delta ( ; uppercase Δ, lowercase δ; , ''délta'', ) is the fourth letter of the Greek alphabet. In the system of Greek numerals, it has a value of four. It was derived from the Phoenician alphabet, Phoenician letter Dalet (letter), dalet 𐤃. Letters that come from delta include the Latin alphabet, Latin D and the Cyrillic script, Cyrillic De (Cyrillic), Д. A river delta (originally, the Nile Delta, delta of the Nile River) is named so because its shape approximates the triangular uppercase letter delta. Contrary to a popular legend, this use of the word ''delta'' was not coined by Herodotus. Pronunciation In Ancient Greek, delta represented a voiced dental plosive . In Modern Greek, it represents a voiced dental fricative , like the "''th''" in "''that''" or "''this''" (while in foreign words is instead commonly transcribed as ντ). Delta is romanization of Greek, romanized as ''d'' or ''dh''. Uppercase The uppercase letter Δ is used to denote: * Change of any changeable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reference Ellipsoid
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations. It is a spheroid (an ellipsoid of revolution) whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation. The ellipsoid is defined by the ''equatorial axis'' () and the ''polar axis'' (); their radial difference is slightly more than 21 km, or 0.335% of (which is not quite 6,400 km). Many methods exist for determination of the axes of an Earth ellipsoid, ranging from meridian arcs up to modern satellite geodesy or the analysis and interconnection of continental geodetic networks. Amongst the different set of data used in national surveys are several of special importance: the Bessel ellipsoid of 1841, the international Hayfo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Series
In mathematics, the binomial series is a generalization of the binomial formula to cases where the exponent is not a positive integer: where \alpha is any complex number, and the power series on the right-hand side is expressed in terms of the (generalized) binomial coefficients :\binom = \frac. The binomial series is the MacLaurin series for the function f(x)=(1+x)^\alpha. It converges when , x, - 1 is assumed. On the other hand, the series does not converge if , x, =1 and \operatorname(\alpha) \le - 1 , again by formula (). Alternatively, we may observe that for all j, \left, \fracj - 1 \ \ge 1 - \fracj \ge 1 . Thus, by formula (), for all k, \left, \ \ge 1 . This completes the proof of (iii). Turning to (iv), we use identity () above with x=-1 and \alpha-1 in place of \alpha, along with formula (), to obtain :\sum_^n \! (-1)^k = \! (-1)^n= \frac1 (1+o(1)) as n\to\infty. Assertion (iv) now follows from the asymptotic behavior of the sequence n^ = e^. (Precisely, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Federal Communications Commission
The Federal Communications Commission (FCC) is an independent agency of the United States government that regulates communications by radio, television, wire, internet, wi-fi, satellite, and cable across the United States. The FCC maintains jurisdiction over the areas of broadband access, fair competition, radio frequency use, media responsibility, public safety, and homeland security. The FCC was established pursuant to the Communications Act of 1934 to replace the radio regulation functions of the previous Federal Radio Commission. The FCC took over wire communication regulation from the Interstate Commerce Commission. The FCC's mandated jurisdiction covers the 50 states, the District of Columbia, and the territories of the United States. The FCC also provides varied degrees of cooperation, oversight, and leadership for similar communications bodies in other countries in North America. The FCC is funded entirely by regulatory fees. It has an estimated fiscal-2022 budg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geographic Coordinate Conversion
In geodesy, conversion among different geographic coordinate systems is made necessary by the different geographic coordinate systems in use across the world and over time. Coordinate conversion is composed of a number of different types of conversion: format change of geographic coordinates, conversion of coordinate systems, or transformation to different geodetic datums. Geographic coordinate conversion has applications in cartography, surveying, navigation and geographic information systems. In geodesy, geographic coordinate ''conversion'' is defined as translation among different coordinate formats or map projections all referenced to the same geodetic datum. A geographic coordinate ''transformation'' is a translation among different geodetic datums. Both geographic coordinate conversion and transformation will be considered in this article. This article assumes readers are already familiar with the content in the articles geographic coordinate system and geodetic datum. Cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth Radius
Earth radius (denoted as ''R''🜨 or ''R''E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted ''a'') of about to a minimum (polar radius, denoted ''b'') of nearly . A globally-average value is usually considered to be with a 0.3% variability (±10 km) for the following reasons. The International Union of Geodesy and Geophysics (IUGG) provides three reference values: the ''mean radius'' (''R'') of three radii measured at two equator points and a pole; the ''authalic radius'', which is the radius of a sphere with the same surface area (''R''); and the ''volumetric radius'', which is the radius of a sphere having the same volume as the ellipsoid (''R''). All three values are about . Other ways to define and measure the Earth's radius involve either the spheroid's radius of curvature or the actual topography. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle Inequality
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. This statement permits the inclusion of Degeneracy (mathematics)#Triangle, degenerate triangles, but some authors, especially those writing about elementary geometry, will exclude this possibility, thus leaving out the possibility of equality. If , , and are the lengths of the sides of a triangle then the triangle inequality states that :c \leq a + b , with equality only in the degenerate case of a triangle with zero area. In Euclidean geometry and some other geometries, the triangle inequality is a theorem about vectors and vector lengths (Norm (mathematics), norms): :\, \mathbf u + \mathbf v\, \leq \, \mathbf u\, + \, \mathbf v\, , where the length of the third side has been replaced by the length of the vector sum . When and are real numbers, they can be viewed as vectors in \R^1, and the triang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vantage-point Tree
A vantage-point tree (or VP tree) is a metric tree that segregates data in a metric space by choosing a position in the space (the "vantage point") and partitioning the data points into two parts: those points that are nearer to the vantage point than a threshold, and those points that are not. By recursively applying this procedure to partition the data into smaller and smaller sets, a tree data structure is created where neighbors in the tree are likely to be neighbors in the space. One generalization is called a multi-vantage-point tree (or MVP tree): a data structure for indexing objects from large metric spaces for similarity search queries. It uses more than one point to partition each level. History Peter Yianilos claimed that the vantage-point tree was discovered independently by him (Peter Yianilos) and by Jeffrey Uhlmann. Yet, Uhlmann published this method before Yianilos in 1991. Uhlmann called the data structure a metric tree, the name VP-tree was proposed by Yianilo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geographical Distance
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. This distance is an element in solving the Geodesy#Geodetic problems, second (inverse) geodetic problem. Introduction Calculating the distance between geographical coordinates is based on some level of abstraction; it does not provide an ''exact'' distance, which is unattainable if one attempted to account for every irregularity in the surface of the Earth. Common abstractions for the surface between two geographic points are: *Flat surface; *Spherical surface; *Ellipsoidal surface. All abstractions above ignore changes in elevation. Calculation of distances which account for changes in elevation relative to the idealized surface are not discussed in this article. Classification of Formulae based on Appr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartography
Cartography (; from , 'papyrus, sheet of paper, map'; and , 'write') is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an imagined reality) can be modeled in ways that communicate spatial information effectively. The fundamental objectives of traditional cartography are to: * Set the map's agenda and select traits of the object to be mapped. This is the concern of map editing. Traits may be physical, such as roads or land masses, or may be abstract, such as toponyms or political boundaries. * Represent the terrain of the mapped object on flat media. This is the concern of map projections. * Eliminate the mapped object's characteristics that are irrelevant to the map's purpose. This is the concern of Cartographic generalization, generalization. * Reduce the complexity of the characteristics that will be mapped. This is also the concern of generalization. * Orchestrate the elements ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Map Projection
In cartography, a map projection is any of a broad set of Transformation (function) , transformations employed to represent the curved two-dimensional Surface (mathematics), surface of a globe on a Plane (mathematics), plane. In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. All projections of a sphere on a plane necessarily distort the surface in some way. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. The study of map projections is primarily about the characterization of their distortions. There is no limit to the number of possible map projections. More generally, proje ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
