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In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point: the projection point. Where it is defined, the mapping is smooth and bijective. It is conformal, meaning that it preserves angles. It is neither isometric nor area-preserving: that is, it preserves neither distances nor the areas of figures. Intuitively, then, the stereographic projection is a way of picturing the sphere as the plane, with some inevitable compromises. Because the sphere and the plane appear in many areas of mathematics and its applications, so does the stereographic projection; it finds use in diverse fields including complex analysis, cartography, geology, and photography. In practice, the projection is carried out by computer or by hand using a special kind of graph paper called a stereographic net, shortened to stereonet or Wulff net. ==History== The stereographic projection was known to Hipparchus, Ptolemy and probably earlier to the Egyptians. It was originally known as the planisphere projection.〔Snyder (1993).〕 ''Planisphaerium'' by Ptolemy is the oldest surviving document that describes it. One of its most important uses was the representation of celestial charts.〔 The term ''planisphere'' is still used to refer to such charts. It is believed that the earliest existing world map, created in 1507 by Gualterius Lud of Saint-Dié, is based upon the stereographic projection, mapping each hemisphere as a circular disk.〔According to (Snyder 1993), although he acknowledges he did not personally see it〕 The equatorial aspect of the stereographic projection, commonly used for maps of the Eastern and Western Hemispheres in the 17th and 18th centuries (and 16th century - Jean Roze 1542; Rumold Mercator 1595),〔Snyder (1989).〕 was utilised by the ancient astronomers like Ptolemy.〔Brown, Lloyd Arnold : (''The story of maps'', p.59 ).〕 François d'Aiguillon gave the stereographic projection its current name in his 1613 work ''Opticorum libri sex philosophis juxta ac mathematicis utiles'' (Six Books of Optics, useful for philosophers and mathematicians alike).〔According to (Elkins, 1988) who references Eckert, "Die Kartenwissenschaft", Berlin 1921, pp 121–123〕 In 1695, Edmond Halley, motivated by his interest in star charts, published the first mathematical proof that this map is conformal.〔Timothy Feeman. 2002. "Portraits of the Earth: A Mathematician Looks at Maps". American Mathematical Society.〕 He used the recently established tools of calculus, invented by his friend Isaac Newton. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「stereographic projection」の詳細全文を読む スポンサード リンク
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