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 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)} )

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