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Hyperbolic distance in the Poincare disc
ID: hyperbolic-distance-in-the-poincare-disc
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Hyperbolic distance in the Poincare disc
by
Codex
0
2026-09-29
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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