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Gott, Goldberg and Vanderbei’s double-sided disk map was designed to minimize all six types of map distortions. Not properly "a" map projection because it is on two surfaces instead of one, it consists of two hemispheric equidistant azimuthal projections back-to-back. [5] [6] [7] 1879 Peirce quincuncial: Other Conformal Charles Sanders Peirce
In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. [1] [2] [3] In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane.
The formulas for the spherical orthographic projection are derived using trigonometry.They are written in terms of longitude (λ) and latitude (φ) on the sphere.Define the radius of the sphere R and the center point (and origin) of the projection (λ 0, φ 0).
A spherical Earth is a well-known historical approximation that is satisfactory for geography, astronomy and many other purposes. Several models with greater accuracy (including ellipsoid ) have been developed so that coordinate systems can serve the precise needs of navigation , surveying , cadastre , land use , and various other concerns.
The spherical shape of the Earth was known and measured by astronomers, mathematicians, and navigators from a variety of literate ancient cultures, including the Hellenic World, and Ancient India. Greek ethnographer Megasthenes , c. 300 BC , has been interpreted as stating that the contemporary Brahmans of India believed in a spherical Earth as ...
With a spherical Earth, half the planet is in daylight at any given time and the other half experiences nighttime. When a given location on the spherical Earth is in sunlight, its antipode – the location exactly on the opposite side of Earth – is in darkness. The spherical shape of Earth causes the Sun to rise and set at different times in ...
The projection found on these maps, dating to 1511, was stated by John Snyder in 1987 to be the same projection as Mercator's. [6] However, given the geometry of a sundial, these maps may well have been based on the similar central cylindrical projection, a limiting case of the gnomonic projection, which is the basis for a sundial. Snyder ...
As a conformal projection, it faithfully represents angles everywhere. In addition, in its spherical form, the stereographic projection is the only map projection that renders all small circles as circles. 3D illustration of the geometric construction of the stereographic projection.