Most books and websites define the hyperbolic distance element and the corresponding shortest paths in the upper half plane with no explanation. I found a derivation for them in a book called Visual Complex Analysis by Needham and it relied on mapping the "pseudosphere" onto the upper half plane.(adsbygoogle = window.adsbygoogle || []).push({});

Is there an elementary derivation that just uses complex analysis ?

If so, where ?

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# Hyperbolic distance element

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