Poincaré half-plane model

Summary

Poincaré half-plane model is a mathematical model^[1]. It draws 78 Wikipedia views per month (mathematical_model category, ranking #31 of 75).^[2]

Key Facts

• Poincaré half-plane model is credited with the discovery of Henri Poincaré^[3].
• Poincaré half-plane model's image is recorded as Parallel rays in Poincare model of hyperbolic geometry.svg^[4].
• Poincaré half-plane model's instance of is recorded as mathematical model^[5].
• Poincaré half-plane model's instance of is recorded as Riemannian manifold^[6].
• Poincaré half-plane model's instance of is recorded as hyperbolic space^[7].
• Henri Poincaré is named after Poincaré half-plane model^[8].
• Poincaré half-plane model's Commons category is recorded as Poincaré half-plane models^[9].
• Poincaré half-plane model's time of discovery or invention is recorded as +1882-00-00T00:00:00Z^[10].
• Poincaré half-plane model's Freebase ID is recorded as /m/02cddg^[11].
• Poincaré half-plane model's Encyclopædia Britannica Online ID is recorded as topic/Poincare-upper-half-plane-model^[12].
• Poincaré half-plane model's different from is recorded as Poincaré disk model^[13].
• Poincaré half-plane model's defining formula is recorded as \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}^[14].
• Poincaré half-plane model's Microsoft Academic ID is recorded as 34948523^[15].
• Poincaré half-plane model's in defining formula is recorded as \mathrm ds^2^[16].

Body

Designation and Status

Recorded instance of include mathematical model^[5], Riemannian manifold^[6], and hyperbolic space^[7].

History and Context

Henri Poincaré is named after Poincaré half-plane model^[8].

Why It Matters

Poincaré half-plane model draws 78 Wikipedia views per month (mathematical_model category, ranking #31 of 75).^[2] It has Wikipedia articles in 10 language editions, a strong signal of global cultural recognition.^[17] It is known by 21 alternative names across languages and contexts.^[18]