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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