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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 ...
As noted above, the iterative solution to the inverse problem fails to converge or converges slowly for nearly antipodal points. An example of slow convergence is (Φ 1, L 1) = (0°, 0°) and (Φ 2, L 2) = (0.5°, 179.5°) for the WGS84 ellipsoid. This requires about 130 iterations to give a result accurate to 1 mm. Depending on how the inverse ...
Noting that sin ( π 2 − φ) = cos (φ), the haversine formula immediately follows. To derive the law of haversines, one starts with the spherical law of cosines: As mentioned above, this formula is an ill-conditioned way of solving for c when c is small. Instead, we substitute the identity that cos (θ) = 1 − 2 hav (θ), and also ...
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 between the two points on the surface of the sphere. (By comparison, the shortest path passing through the sphere's interior is the chord between ...
Friction of distance. Friction of distance is a core principle of geography that states that movement incurs some form of cost, in the form of physical effort, energy, time, and/or the expenditure of other resources, and that these costs are proportional to the distance traveled. This cost is thus a resistance against movement, analogous (but ...
Mercator 1569 world map (Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata) showing latitudes 66°S to 80°N. The Mercator projection (/ mərˈkeɪtər /) is a conformal cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for ...
Distance decay is a geographical term which describes the effect of distance on cultural or spatial interactions. [1] The distance decay effect states that the interaction between two locales declines as the distance between them increases. Once the distance is outside of the two locales' activity space, their interactions begin to decrease.
Triangulation of Kodiak Island in Alaska in 1929. In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed baseline by using trigonometry, rather than measuring distances to the point directly as in trilateration.