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Earth's authalic radius (meaning "equal area") is the radius of a hypothetical perfect sphere that has the same surface area as the reference ellipsoid. The IUGG denotes the authalic radius as R 2. [2] A closed-form solution exists for a spheroid: [8]
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The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an oblate ellipsoid, a slightly flattened sphere. A geodesic is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface.
In cartography, an equivalent, authalic, or equal-area projection is a map projection that preserves relative area measure between any and all map regions. Equivalent projections are widely used for thematic maps showing scenario distribution such as population, farmland distribution, forested areas, and so forth, because an equal-area map does ...
The 1980 Geodetic Reference System (GRS 80) posited a 6 378 137 m semi-major axis and a 298.257222101 flattening. This system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics (IUGG) in Canberra, Australia, 1979. The GRS 80 reference system was originally used by the World Geodetic System 1984 (WGS 84).
The authalic radius is an surface area-equivalent radius for solid figures such as an ellipsoid. The osculating circle and osculating sphere define curvature -equivalent radii at a particular point of tangency for plane figures and solid figures, respectively.
An approximation of the AuthaGraph projection. AuthaGraph is an approximately equal-area world map projection invented by Japanese architect Hajime Narukawa [1] in 1999. [2] The map is made by equally dividing a spherical surface into 96 triangles, transferring it to a tetrahedron while maintaining area proportions, and unfolding it in the form of a rectangle: it is a polyhedral map projection.
Equal-area. Walter Behrmann. Cylindrical equal-area projection with standard parallels at 30°N/S and an aspect ratio of (3/4)π ≈ 2.356. 2002. Hobo–Dyer. Cylindrical. Equal-area. Mick Dyer. Cylindrical equal-area projection with standard parallels at 37.5°N/S and an aspect ratio of 1.977.