Beltrami–Klein model

Target entity: Beltrami–Klein model
Context triple: [Non-Euclidean geometry, hasModel, Beltrami–Klein model]

• A. Poincaré upper half-plane model
  The Poincaré upper half-plane model is a standard representation of the hyperbolic plane using the complex numbers with positive imaginary part, equipped with a specific metric that makes geodesics appear as semicircles and vertical lines.
• B. Poincaré metric
  The Poincaré metric is the canonical complete Riemannian metric of constant negative curvature on simply connected Riemann surfaces like the unit disk or upper half-plane, fundamental in complex analysis and hyperbolic geometry.
• C. Möbius geometry
  Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
• D. Riemann sphere
  The Riemann sphere is the complex plane plus a point at infinity, forming a one-dimensional complex manifold topologically equivalent to a sphere and used to study meromorphic functions and complex analysis.
• E. Busemann
  Busemann is a surname most notably associated with Herbert Busemann, a German-American mathematician known for his work in geometry.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Beltrami–Klein model
Target entity description: The Beltrami–Klein model is a projective representation of hyperbolic geometry in which the entire hyperbolic plane is mapped inside a disk and geodesics appear as straight line segments.

• A. Poincaré upper half-plane model
  The Poincaré upper half-plane model is a standard representation of the hyperbolic plane using the complex numbers with positive imaginary part, equipped with a specific metric that makes geodesics appear as semicircles and vertical lines.
• B. Poincaré metric
  The Poincaré metric is the canonical complete Riemannian metric of constant negative curvature on simply connected Riemann surfaces like the unit disk or upper half-plane, fundamental in complex analysis and hyperbolic geometry.
• C. Möbius geometry
  Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
• D. Riemann sphere
  The Riemann sphere is the complex plane plus a point at infinity, forming a one-dimensional complex manifold topologically equivalent to a sphere and used to study meromorphic functions and complex analysis.
• E. Busemann
  Busemann is a surname most notably associated with Herbert Busemann, a German-American mathematician known for his work in geometry.
• F. None of above. chosen