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Thus the Gaussian curvature is an intrinsic invariant of a surface. Gauss presented the theorem in this manner (translated from Latin): Thus the formula of the preceding article leads itself to the remarkable Theorem. If a curved surface is developed upon any other surface whatever, the measure of curvature in each point remains unchanged.
The Old Bedford River, photographed from the bridge at Welney, Norfolk (2008); the camera is looking downstream, south-west of the bridge. The Bedford Level experiment was a series of observations carried out along a 6-mile (10 km) length of the Old Bedford River on the Bedford Level of the Cambridgeshire Fens in the United Kingdom during the 19th and early 20th centuries to deny the curvature ...
Medieval artistic representation of a spherical Earth – with compartments representing earth, air, and water (c. 1400) The Erdapfel, the oldest surviving terrestrial globe (1492/1493) The spherical shape of the Earth was known and measured by astronomers, mathematicians, and navigators from a variety of literate ancient cultures, including ...
Snell calculated how the planar formulae could be corrected to allow for the curvature of the earth. He also showed how to resection, or calculate, the position of a point inside a triangle using the angles cast between the vertices at the unknown point. These could be measured much more accurately than bearings of the vertices, which depended ...
Roundness is an important indicator of the genetic affiliation of a clastic rock.The degree of roundness points to the range and mode of transport of clastic material, and can also serve as a search criterion in mineral exploration, especially for placer deposits.
A data set which describes the global average of the Earth's surface curvature is called the mean Earth Ellipsoid. It refers to a theoretical coherence between the geographic latitude and the meridional curvature of the geoid. The latter is close to the mean sea level, and therefore an ideal Earth ellipsoid has the same volume as the geoid.
In Riemannian geometry, the geodesic curvature of a curve measures how far the curve is from being a geodesic. For example, for 1D curves on a 2D surface embedded in 3D space , it is the curvature of the curve projected onto the surface's tangent plane.
Tortuosity calculation from an x-ray tomography reconstruction of a porous sandstone (the pores are shown): [9] the color represents the shortest distance within the pore space from the left limit of the image to any point in the pores. Comparing this distance to the straight-line distance shows that the tortuosity is about 1.5 for this sample.