Poincaré disk model

Target entity: Poincaré disk model
Context triple: [Non-Euclidean geometry, hasModel, Poincaré disk 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. 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.
• D. Soddy circle
  A Soddy circle is one of the circles in a configuration of four mutually tangent circles, central to the geometric problem described by Descartes' circle theorem.
• E. Cartesian circle
  The Cartesian circle is a famous alleged circular reasoning in René Descartes’ Meditations, where his proof of God’s existence and his justification of clear and distinct perceptions appear to depend on each other.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Poincaré disk model
Target entity description: The Poincaré disk model is a representation of hyperbolic geometry in which the entire infinite hyperbolic plane is mapped inside a unit disk, with geodesics appearing as circular arcs orthogonal to the boundary.

• 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. 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.
• D. Soddy circle
  A Soddy circle is one of the circles in a configuration of four mutually tangent circles, central to the geometric problem described by Descartes' circle theorem.
• E. Cartesian circle
  The Cartesian circle is a famous alleged circular reasoning in René Descartes’ Meditations, where his proof of God’s existence and his justification of clear and distinct perceptions appear to depend on each other.
• F. None of above. chosen