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The maturation of complex analysis led to general techniques for conformal mapping, where points of a flat surface are handled as numbers on the complex plane.While working at the United States Coast and Geodetic Survey, the American philosopher Charles Sanders Peirce published his projection in 1879, [2] having been inspired by H. A. Schwarz's 1869 conformal transformation of a circle onto a ...
Equirectangular projection of the world; the standard parallel is the equator (plate carrée projection). Equirectangular projection with Tissot's indicatrix of deformation and with the standard parallels lying on the equator True-colour satellite image of Earth in equirectangular projection Height map of planet Earth at 2km per pixel, including oceanic bathymetry information, normalized as 8 ...
The Arctic Circle is roughly 16,000 km (9,900 mi) long, as is the Antarctic Circle. [23] A "true circumnavigation" of Earth is defined, in order to account for the shape of Earth, to be about 2.5 times as long, including a crossing of the equator, at about 40,000 km (25,000 mi). [24]
The equator is the circle of latitude that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude , about 40,075 km (24,901 mi) in circumference, halfway between the North and South poles. [ 1 ]
To find the way-points, that is the positions of selected points on the great circle between P 1 and P 2, we first extrapolate the great circle back to its node A, the point at which the great circle crosses the equator in the northward direction: let the longitude of this point be λ 0 — see Fig 1.
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
Positions on the great circle of radius are parametrized by arc length measured from the northward crossing of the equator. The great ellipse has a semi-axes a {\displaystyle a} and a 1 − e 2 cos 2 γ 0 {\displaystyle a{\sqrt {1-e^{2}\cos ^{2}\gamma _{0}}}} , where γ 0 {\displaystyle \gamma _{0}} is the great-circle azimuth at the ...
If A lies on the equator, φ 1 = 0, this relation is exact and as a consequence the equator is only a shortest geodesic if |λ 12 | ≤ π (1 − f). For a prolate ellipsoid, the cut locus is a segment of the anti-meridian centered on the point antipodal to A , λ 12 = π , and this means that meridional geodesics stop being shortest paths ...