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The Mercator projection preserves angles but fails to preserve area, hence the massive distortion of Antarctica. Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major result of differential geometry , proved by Carl Friedrich Gauss in 1827, that concerns the curvature of surfaces.
This six-fold category characterisation is used in the Shepard and Young comparison chart and the Powers chart but the Krumbein chart has nine categories. Rounding of sediment particles can indicate the distance and time involved [ citation needed ] in the transportation of the sediment from the source area to where it is deposited .
Equal-area Krzysztof M. Górski: Hybrid of Collignon + Lambert cylindrical equal-area. 1929 Boggs eumorphic: Pseudocylindrical Equal-area Samuel Whittemore Boggs The equal-area projection that results from average of sinusoidal and Mollweide y-coordinates and thereby constraining the x coordinate. 1929 Craster parabolic =Putniņš P4 ...
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.
The product k 1 k 2 of the two principal curvatures is the Gaussian curvature, K, and the average (k 1 + k 2)/2 is the mean curvature, H. If at least one of the principal curvatures is zero at every point, then the Gaussian curvature will be 0 and the surface is a developable surface. For a minimal surface, the mean curvature is zero at every ...
where the normal chosen affects the sign of the curvature. The sign of the curvature depends on the choice of normal: the curvature is positive if the surface curves "towards" the normal. The formula above holds for surfaces in 3D space defined in any manner, as long as the divergence of the unit normal may be calculated. Mean Curvature may ...
In the 19th century, many astronomers and geodesists were engaged in detailed studies of the Earth's curvature along different meridian arcs. The analyses resulted in a great many model ellipsoids such as Plessis 1817, Airy 1830, Bessel 1841, Everest 1830, and Clarke 1866. [31] A comprehensive list of ellipsoids is given under Earth ellipsoid.
A cube map projection of the Earth, similar to QSC but not equal-area. There are some related projections: rHEALPix: is a cubic configuration in the HEALPix framework (of 2003), elaborated in 2016. [5] S2 projection was created at Google (published in 2016 with a first pre-release in 2019) for the purpose of defining a discrete global grid ...