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A hyperbolic sector is a region of the Cartesian plane bounded by rays from the origin to two points (''a'', 1/''a'') and (''b'', 1/''b'') and by the rectangular hyperbola ''xy'' = 1 (or the corresponding region when this hyperbola is rescaled and its orientation is altered by a rotation leaving the center at the origin, as with the unit hyperbola). A hyperbolic sector in standard position has ''a'' = 1 and ''b'' > 1 . Hyperbolic sectors are the basis for the hyperbolic functions. ==Area== The area of a hyperbolic sector in standard position is ln ''b'' . Proof: Integrate under 1/''x'' from 1 to ''b'', add triangle , and subtract triangle . 〔V.G. Ashkinuse & Isaak Yaglom (1962) ''Ideas and Methods of Affine and Projective Geometry'' (in Russian), page 151, Ministry of Education, Moscow〕 When in standard position, a hyperbolic sector corresponds to a positive hyperbolic angle at the origin, with the measure of the latter being defined as the area of the former. 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「Hyperbolic sector」の詳細全文を読む スポンサード リンク
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