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Mollweide's Projection: Equal-Area Global Map

Learn about Mollweide's projection - an equal-area, pseudocylindrical map widely used for global maps. Discover its history, variations, and applications.

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Mollweide's Projection: Equal-Area Global Map

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  1. Mollweide's Projection Dr. Salve P. N. • M.A.,SET, Ph.D. • Maharaja JivajiroShindeMahavidyalyaShrigonda • Dist : Ahmednagar

  2. Mollweide's Projection Created by the German Karl B. Mollweide, the eponymous pseudocylindrical projection is bounded by an ellipse; poles are points and its Equator is twice as long as the straight central meridian, but neither is a standard line. All other meridians are elliptical arcs, and parallels are unequally spaced in order to preserve areas. Only the intersections of the central meridian with the standard parallels 40°44'12"N and S are free of distortion. Even though its geometry is easily deduced, calculation is more complex than for the other classic pseudocylindrical still important today, the sinusoidal — this and the loss of uniform scale along the central meridian are the price paid for lesser crowding in polar areas. Despite the equal area property and its pleasant shape, Mollweide's projection received little recognition since publication in 1805, becoming better known only after the French Jacques Babinet presented it as the homalographic in 1857. Historically, its other common aliases include elliptical, Babinet, homolographic (from the Greek homo for "same", thus equal-area).

  3. Profoundly influential, this projection was combined with the sinusoidal in fused (John P. Goode's homolosine, Allen K. Philbrick'sSinu-Mollweide, GyörgyÉrdi-Krausz) and averaged (Samuel W. Boggs and Oscar S. Adams's eumorphic; some authors also relate it to the WinkelII) designs. Interrupted variants, alone or combined, have also been popular. Other variations include oblique aspects like John Bartholomew's Atlantis and simple rescaling by orthogonal reciprocal factors, which preserves areal equivalence while changing both aspect ratio and the angular distortion pattern. For instance, Waldo Tobler (1962) suggested making the whole map circular with standard parallels 73°7'43.85" N and S; Robert H. Bromley's projection (1965) elongates the ellipse merging the standard parallels at the Equator. Mollweide's 2:1 ellipse is occasionally mistaken for Aitoff's and Hammer's projections, neither of which are pseudocylindricals, although the latter is also equal-area. Much more easily confused is an elliptical full-world extension of Apian's second globular projection, mathematically much simpler and not equal-area.

  4. Mollweide projection • The Mollweide projection is an equal-area, pseudocylindrical map projection generally used for global maps of the world or night sky. It is also known as the Babinet projection, homalographic projection, homolographic projection, and elliptical projection. The projection trades accuracy of angle and shape for accuracy of proportions in area, and as such is used where that property is needed, such as maps depicting global distributions. • The projection was first published by mathematician and astronomer Karl (or Carl) BrandanMollweide (1774–1825) of Leipzig in 1805. It was reinvented and popularized in 1857 by Jacques Babinet, who gave it the name homalographic projection. The variation homolographic arose from frequent nineteenth-century usage in star atlases.[

  5. The Mollweide is a pseudocylindrical projection in which the equator is represented as a straight horizontal line perpendicular to a central meridian one-half its length. The other parallels compress near the poles, while the other meridians are equally spaced at the equator. The meridians at 90 degrees east and west form a perfect circle, and the whole earth is depicted in a proportional 2:1 ellipse. The proportion of the area of the ellipse between any given parallel and the equator is the same as the proportion of the area on the globe between that parallel and the equator, but at the expense of shape distortion, which is significant at the perimeter of the ellipse, although not as severe as in the sinusoidal projection. • Shape distortion may be diminished by using an interrupted version. A sinusoidal interruptedMollweide projection discards the central meridian in favor of alternating half-meridians which terminate at right angles to the equator. This has the effect of dividing the globe into lobes. In contrast, a parallel interruptedMollweide projection uses multiple disjoint central meridians, giving the effect of multiple ellipses joined at the equator. More rarely, the projection can be drawn obliquely to shift the areas of distortion to the oceans, allowing the continents to remain truer to form. • The Mollweide, or its properties, has inspired the creation of several other projections, including the Goode's homolosine, van der Grinten and the Boggs eumorphic.[

  6. Normal Mollweide map Rescaled Mollweide projections by Bromley (above, with standard Equator) and Tobler (on the right, circular) are equal-area too

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