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Hyperbolic sector

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A '''hyperbolic sector''' is a region of the Cartesian plane {(''x'',''y'')} bounded by rays from the origin to two points (''a'',1/''a'') and (b,1/''b'') and by the hyperbola ''xy'' = 1. A hyperbolic sector in standard position has ''a'' = 1 and ''b'' > 1 . The area of a hyperbolic sector in standard position is natural logarithm log ''b'' . (proof: integrate under 1/''x'' from 1 to ''b'', add triangle {(0,0),(1,0),(1,1)}, and subtract triangle {(0,0),(''b'',0),(''b'',1/''b'')} ) {{math-stub}} Category:Curves Category:Elementary geometry