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Mercator 1569 world map ( Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata) showing latitudes 66°S to 80°N. The Mercator projection ( / mərˈkeɪtər /) is a conformal cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for ...
Earth radius (denoted as R 🜨 or R E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted a) of nearly 6,378 km (3,963 mi) to a minimum (polar radius, denoted b) of nearly 6,357 km (3,950 mi).
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection ), onto a plane (the projection plane) perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the center of projection to the ...
The study of map projections is primarily about the characterization of their distortions. There is no limit to the number of possible map projections. [ 7]: 1 More generally, projections are considered in several fields of pure mathematics, including differential geometry, projective geometry, and manifolds. However, the term "map projection ...
Umbra, penumbra and antumbra of Earth and images that could be seen at some points in these areas (Note: the relative size and distance of the bodies shown are not to scale.)“… The Earth’s shadow has two distinct parts,… the UMBRA is the part of the shadow where all direct sunlight is blocked by the Earth; the PENUMBRA of the shadow is ...
Orthographic projection in cartography has been used since antiquity. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective (or azimuthal) projection in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic projection is at infinite distance.
The latitude of the circle is approximately the angle between the Equator and the circle, with the angle's vertex at Earth's centre. The Equator is at 0°, and the North Pole and South Pole are at 90° north and 90° south, respectively. The Equator is the longest circle of latitude and is the only circle of latitude which also is a great circle.
Cyclocycloid. A cyclocycloid is a roulette traced by a point attached to a circle of radius r rolling around, a fixed circle of radius R, where the point is at a distance d from the center of the exterior circle. The red curve is a cyclocycloid (in this case an hypocycloid) drawn as the smaller black circle rolls around inside the larger blue ...
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