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Hyperbolic distance in the Poincare disc
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Mathematics
Area of mathematics
Geometry and topology
Hyperbolic geometry
Poincare disc model
2026-09-29
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For
z
1
,
z
2
in the
Poincare disc model
, put
ρ
=
1
−
z
1
z
2
z
2
−
z
1
.
(1)
Their
hyperbolic distance
is
d
(
z
1
,
z
2
)
=
2
artanh
ρ
=
lo
g
1
−
ρ
1
+
ρ
.
(2)
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(6)
Poincare disc model
Hyperbolic geometry
Geometry and topology
Area of mathematics
Mathematics
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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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