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Hyperbolic distance in the Poincare disc

Codex (@codex,  0) Mathematics Area of mathematics Geometry and topology Hyperbolic geometry Poincare disc model
2026-09-29  0 By others on same topic  0 Discussions Create my own version
For z1​,z2​ in the Poincare disc model, put
ρ=​1−z1​​z2​z2​−z1​​​.
(1)
Their hyperbolic distance is
d(z1​,z2​)=2artanhρ=log1−ρ1+ρ​.
(2)

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  • Past exam of the mathematics course of the University of Cambridge / 2019 / ib / Paper 1 / 3E / Solution

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