Geographical Distance

picture info	Geographical Distance Geographical distance or geodetic distance is the distance measured along the surface of the earth. 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. Nomenclature Distance, D,\,\! is calculated between two points, P_1\,\! and P_2\,\!. The geograph ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]
	Roßberg Alpen 1 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) (869 m), a mountain in the Swabian Jura, Baden-Württemberg, Germany * Roßberg (Hinterland) (497.1 m), a hill in the Gladenbach Uplands, Hesse, Germany {{dab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	N-vector The ''n''-vector representation (also called geodetic normal or ellipsoid normal vector) is a three-parameter non-singular representation well-suited for replacing geodetic coordinates (latitude and longitude) for horizontal position representation in mathematical calculations and computer algorithms. Geometrically, the ''n''-vector for a given position on an ellipsoid is the outward-pointing unit vector that is normal in that position to the ellipsoid. For representing horizontal positions on Earth, the ellipsoid is a reference ellipsoid and the vector is decomposed in an Earth-centered Earth-fixed coordinate system. It behaves smoothly at all Earth positions, and it holds the mathematical one-to-one property. More in general, the concept can be applied to representing positions on the boundary of a strictly convex bounded subset of ''k''-dimensional Euclidean space, provided that that boundary is a differentiable manifold. In this general case, the ''n''-vector consist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Geodesic In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line". The noun '' geodesic'' and the adjective ''geodetic'' come from ''geodesy'', the science of measuring the size and shape of Earth, though many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between two points on the Earth's surface. For a spherical Earth, it is a segment of a great circle (see also great-circle distance). The term has since been generalized to more abstract mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph. In a Riemannian manifold or submanifold, geodesics are characterised by the property of having vanishin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Long Geodesic On An Oblate Ellipsoid Long may refer to: Measurement * Long, characteristic of something of great time, duration * Long, characteristic of something of great length * Longitude (abbreviation: long.), a geographic coordinate * Longa (music), note value in early music mensural notation Places Asia * Long District, Laos * Long District, Phrae, Thailand * Longjiang (other) or River Long (lit. "dragon river"), one of several rivers in China * Yangtze River or Changjiang (lit. "Long River"), China Elsewhere * Long, Somme, France * Long, Washington, United States People * Long (surname) * Long (surname 龍) (Chinese surname) Fictional characters * Long (Bloody Roar), Long (''Bloody Roar''), in the video game series Sports * Long, a Fielding (cricket)#Modifiers, fielding term in cricket * Long, in tennis and similar games, beyond the service line during a serve and beyond the baseline during play Other uses * , a U.S. Navy ship name * Long (finance), a position in finance, especially stock marke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Great-circle Distance The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle. It is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior). The distance between two points in Euclidean space is the length of a straight line between them, but on the sphere there are no straight lines. In spaces with curvature, straight lines are replaced by geodesics. Geodesics on the sphere are circles on the sphere whose centers coincide with the center of the sphere, and are called 'great circles'. The determination of the great-circle distance is part of the more general problem of great-circle navigation, which also computes the azimuths at the end points and intermediate way-points. Through any two points on a sphere that are not antipodal points (directly opposite each other), there is a unique great circle. The two points separate the gre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Spherical Trigonometry Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam. The subject came to fruition in Early Modern times with important developments by John Napier, Delambre and others, and attained an essentially complete form by the end of the nineteenth century with the publication of Todhunter's textbook ''Spherical trigonometry for the use of colleges and Schools''. Since then, significant developments have been the application of vector methods, quaternion methods, and the use of numerical methods. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Chebyshev Polynomials The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T_n(x) and U_n(x). They can be defined in several equivalent ways, one of which starts with trigonometric functions: The Chebyshev polynomials of the first kind T_n are defined by : T_n(\cos \theta) = \cos(n\theta). Similarly, the Chebyshev polynomials of the second kind U_n are defined by : U_n(\cos \theta) \sin \theta = \sin\big((n + 1)\theta\big). That these expressions define polynomials in \cos\theta may not be obvious at first sight, but follows by rewriting \cos(n\theta) and \sin\big((n+1)\theta\big) using de Moivre's formula or by using the angle sum formulas for \cos and \sin repeatedly. For example, the double angle formulas, which follow directly from the angle sum formulas, may be used to obtain T_2(\cos\theta)=\cos(2\theta)=2\cos^2\theta-1 and U_1(\cos\theta)\sin\theta=\sin(2\theta)=2\cos\theta\sin\theta, which are respectively a polynomial in \cos\th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	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'' (''a'') and the ''polar axis'' (''b''); their radial difference is slightly more than 21 km, or 0.335% of ''a'' (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 H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Binomial Series In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like (1+x)^n for a nonnegative integer n. Specifically, the binomial series is the Taylor series for the function f(x)=(1+x)^ centered at x = 0, where \alpha \in \Complex and , x, 0 and diverges to +\infty if \operatorname\alpha<0. If $\operatorname\alpha=0$ , then $n^ = e^$ converges if and only if the sequence $\operatorname\alpha\log n$ converges $\bmod$ , which is certainly true if $\alpha=0$ but false if $\operatorname\alpha \neq0$ : in the latter case the sequence is dense $\bmod$ , due to the fact that $\log n$ diverges and $\log (n+1)-\log n$ converges to zero). Summation of the binomial series The usual argument to compute the sum of the binomial series goes as follows. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Radius Of Curvature (applications) In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. Definition In the case of a space curve, the radius of curvature is the length of the curvature vector. In the case of a plane curve, then is the absolute value of : R \equiv \left, \frac \ = \frac, where is the arc length from a fixed point on the curve, is the tangential angle and is the curvature. Formula In 2D If the curve is given in Cartesian coordinates as , i.e., as the graph of a function, then the radius of curvature is (assuming the curve is differentiable up to order 2): : R =\left, \frac \, \qquad\mbox\quad y' = \frac,\quad y'' = \frac, and denotes the absolute value of . If the curve is given parametrically by functions and , then the radius ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Federal Communications Commission The Federal Communications Commission (FCC) is an independent agency of the United States federal government that regulates communications by radio, television, wire, 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 formed by the Communications Act of 1934 to replace the radio regulation functions of the 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 of North America. The FCC is funded entirely by regulatory fees. It has an estimated fiscal-2022 budget of US $388 million. It has 1,482 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Cartography Cartography (; from grc, χάρτης , "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 characteristics of the mapped object that are not relevant to the map's purpose. This is the concern of generalization. * Reduce the complexity of the characteristics that will be mapped. This is also the concern of generalization. * Orchestrate the elements of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]

Summation of the binomial series