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Hi!

I'm trying to derive the hyperbolic distance formula for the upper-half plane model.

It is given here: http://en.wikipedia.org/wiki/Poincar%C3%A9_half-plane_model" [Broken]

I have the first formula, (ds)

But I can't figure out how they got the distance formula below it.

I understand the integral of ds is the distance, but I dont know how they got to arccosh. I've never dealt with hyperbolic trig functions before, so I wonder if that's where I'm running into trouble. I've looked up the hyperbolic trig identities, but I'm unable to get something that when integrated, would result in arccosh. I've also tried taking the derivative of the arccosh function, but I'm not completely sure which variable I should be deriving with respect to.

Please a little advice to get me pointed in the right direction!

Thank you!

I'm trying to derive the hyperbolic distance formula for the upper-half plane model.

It is given here: http://en.wikipedia.org/wiki/Poincar%C3%A9_half-plane_model" [Broken]

I have the first formula, (ds)

^{2}= ...But I can't figure out how they got the distance formula below it.

I understand the integral of ds is the distance, but I dont know how they got to arccosh. I've never dealt with hyperbolic trig functions before, so I wonder if that's where I'm running into trouble. I've looked up the hyperbolic trig identities, but I'm unable to get something that when integrated, would result in arccosh. I've also tried taking the derivative of the arccosh function, but I'm not completely sure which variable I should be deriving with respect to.

Please a little advice to get me pointed in the right direction!

Thank you!

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