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Estimating the height of a mountain using triangulation A triangulation station signed by iron rod [1] In trigonometry and geometry , triangulation is the process of determining the location of a point by forming triangles to the point from known points.
A triangulation station, ... The process of placing trig points on top of prominent hills and mountains began in 1935 to assist in the accurate retriangulation of ...
Triangulation can also refer to the accurate surveying of systems of very large triangles, called triangulation networks. This followed from the work of Willebrord Snell in 1615–17, who showed how a point could be located from the angles subtended from three known points, but measured at the new unknown point rather than the previously fixed ...
Triangulation surveys were based on a few carefully measured baselines and a series of angles. The initial baseline was measured with great care since the accuracy of the subsequent survey was critically dependent upon it. Various corrections were applied, principally temperature.
Closeup of a United States Coast and Geodetic Survey marker. United States Army Corps of Engineers Survey Marker Marker for triangulation station, indicated by triangle in center Reference marker for triangulation station in upper photo A cotton spindle spike in Tel Aviv pavement, used as a marker for public area cadastral surveying.
The analysis has been simplified by considering the attraction on only one side of the mountain. [22] A plumb-bob of mass m is situated a distance d from P, the centre of mass of a mountain of mass M M and density ρ M. It is deflected through a small angle θ due to its attraction F towards P and its weight W directed towards the Earth.
A Euclidean triangulation of a surface is a set of subset of compact spaces of homeomorphic to a non degenerate triangle in via such that they cover the entire surface, the intersection on any pair of subsets is either empty, an edge or a vertex and if the intersection the intersection is not empty then is an isometry of the plane on that ...
In mathematics, triangulation describes the replacement of topological spaces with simplicial complexes by the choice of an appropriate homeomorphism. A space that admits such a homeomorphism is called a triangulable space .