Flattening the Earth: Two Thousand Years of Map Projections

Flattening the Earth: Two Thousand Years of Map Projections

Language: English

Pages: 384

ISBN: 0226767477

Format: PDF / Kindle (mobi) / ePub

As long as there have been maps, cartographers have grappled with the impossibility of portraying the earth in two dimensions. To solve this problem mapmakers have created hundreds of map projections, mathematical methods for drawing the round earth on a flat surface. Yet of the hundreds of existing projections, and the infinite number that are theoretically possible, none is perfectly accurate.

Flattening the Earth is the first detailed history of map projections since 1863. John P. Snyder discusses and illustrates the hundreds of known projections created from 500 B.C. to the present, emphasizing developments since the Renaissance and closing with a look at the variety of projections made possible by computers.

The book contains 170 illustrations, including outline maps from original sources and modern computerized reconstructions. Though the text is not mathematically based, a few equations are included to permit the more technical reader to plot some projections. Tables summarize the features of nearly two hundred different projections and list those used in nineteenth-and twentieth-century atlases.

"This book is unique and significant: a thorough, well-organized, and insightful history of map projections. Snyder is the world's foremost authority on the subject and a significant innovator in his own right."—Mark Monmonier, author of How to Lie with Maps and Mapping It Out: Expository Cartography for the Humanities and Social Sciences.

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First, he placed the point at 1.594 times the radius, solved fro m a lengthy equation to minimize the "entire change of length increase" proceeding 90° out from the center. His second proposal involved a distance of 1.732 or \/3, so that the greatest error in the scale factor along a meridian is as small as possible, with the plane of projection passing through the center of the globe. His third, speci fying certain area stipulations for a central plane, led to a distance of 2. 105 times the

Delisle, or de L'isle, depending on the map) of an illustrious French famil y of mapmakers, and brothe r of the more fa mous Guillaume. H e developed an arrangement with two standard parallels along which the scale is held true, but with details that make it diffe re nt from the mod ern equidistan t or simple conic \vith two standard parallels. O n De )'Isle's p rojection, now obsolete, th e parallels are concentric and equidistant circular arcs, with the central parallel at a radius equal to the

the straight central meridian and as circular arcs each with a radius equal to its radius on a developed cone tangent at that parallel. The meridians are nonuniformly spaced along each parallel except one so that the res ulting meridian curves inte rsect each parallel at right angles, hence the name recta ngular (fig. 3.19). Any parallel other than the pole may be made true to scale. If this parallel is the equator, the resulting for mulas for the sphere may be written x y = = p sin e and Rel>

twice its radius. August claimed that Eisenlohr's projection is too complicated to be practical, and August included a geometrical construction to offset the fac t that his formulas are also complicated. Eisenlohr (1875) responded a year later in considerable detail, complete with tables of scale factors, but August's was the projection discussed much more extensively in the next century. 92 Polyheddc and Polyhedral Prnjections At some time during the nineteenth centu ry, although it is not

it was used only minimally until, during the twentieth century, it became the dominant projection for maps of the United States and some other regions. Th~ U.S. Coast and Geodetic Survey's booklet by 0. S. Adams (1927, 1) contained for the first time ellipsoidal formulas and tables for the Albers, calling the projection "an equal,area representation [of the United States] that is as good as any other and in many respects superior to all others." Adams chose as standard parallels for maps of the

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