Poincaré half-plane model
upper-half plane model of hyperbolic non-Euclidean geometry
Facts
7 properties- Instance of
- mathematical model, Riemannian manifold, hyperbolic space[3][4]
- Defining formula
- \begin{aligned}\mathbb H &=\{(z,\vec x)|z\in\mathbb R^+,\;\vec x\in\mathbb R^d\} \\ \mathrm ds^2&= \frac{\mathrm dz^2 + (\mathrm d\vec x)^2}{z^2}\end{aligned}[8]
- Different from
- Poincaré disk model[7]
- Discoverer or inventor
- Henri Poincaré[2]
- In defining formula
- \mathrm ds^2[9]
- Named after
- Henri Poincaré[5]
- Time of discovery or invention
- 1882[6]
🏷️ Also known as
en Poincaré half-plane
en Poincaré half-plane model
en Poincaré plane
en Poincare half-plane model
de Poincaré-Halbebenenmodell
fr plan de Poincaré
fr demi-plan de Poincaré
he מודל חצי המישור של פואנקרה
it modello del semipiano
it modello del semispazio
it semispazio di Poincaré
ja ポワンカレ上半平面模型
ja ポアンカレの上半平面モデル
ja ポワンカレの上半平面モデル
ja ポワンカレの上半平面模型
ja ポワンカレの半平面モデル
ja ポワンカレの半平面模型
ja ポワンカレ上半平面
ja ポワンカレ半平面
ja ポワンカレ半平面モデル
🔖 Identifiers · 4
- Image (Wikimedia Commons)
- Parallel rays in Poincare model of hyperbolic geometry.svg ↗
- Encyclopædia Britannica Online ID
- topic/Poincare-upper-half-plane-model
- Freebase ID
- /m/02cddg
- Microsoft Academic ID (discontinued)
- 34948523
🔗 Connections
Instance of 3
Created notable works 1
Different from 1
Discoverer or inventor 1
Named after 1
← Different from 1
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Summary
Poincaré half-plane model is a mathematical model[1].