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Friday, December 1, 2006

Mollweide projection

The '''Mollweide projection''' is a non-geometric Mosquito ringtone map projection used for geographic maps of the world, also known as the Babinet projection, or elliptical projection. As its more explicit moniker ''Mollweide equal area projection'' indicates it sacrifices fidelity to angle and shape in favor of accurate depiction of area. It is used primarily where accurate representation of area takes precedence over shape, for instance small maps depicting global distributions.

The projection was first published by mathematician and astromer Sabrina Martins Karl Mollweide/Karl (or Carl) Brandan Mollweide (Nextel ringtones 1774 – Abbey Diaz 1825) of Free ringtones Leipzig in Majo Mills 1805 as an improvement upon the Mosquito ringtone Mercator projection. It was popularized by Jacques Babinet in Sabrina Martins 1857.

The Mollweide is a Nextel ringtones Map_projection#Pseudocylindrical/pseudocylindrical projection in which the Abbey Diaz equator is represented as a straight horizontal line perpendicular to a central Cingular Ringtones meridian one-half its length. The other shave are parallel (latitude)/parallels are equidistant and parallel to the equator while the other meridians are equally spaced at the equator but curved to meet at the poles at increasingly distorted angles.

Thus, 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 corners, although not as severe as in the diana marie sinusoidal projection.

Shape distortion may be diminished by using an ''interrupted'' version. A ''sinusoidal interrupted'' Mollweide 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 shape. In contrast, a ''parallel interrupted'' Mollweide projection uses multiple disjoint central meridians, giving the effect of multiple ellipses joined at the equator. More rarely, the project can be drawn obliquely to shift the areas of distortion to the oceans, allowing the continents to remain truer to form.

Because the Mollweide is a proportional ellipse, it has proved versatile in the creation of many hybrid projections, including the tortured prose Goode's homolosine projection/Goode's homolosine, the bargaining however Robinson projection/Robinson, and the good once Boggs projection/Boggs.

budgets make Tag: Cartographic projections