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On the Poincare disk, a straight line is a circle that intersects the edge of the disk at right angles. Also, angles are preserved – if two “lines” are at 60 degrees, then they stay at 60 degrees even if you move the focus around. So given a line, a point on the line, and an angle, there’s only one circular arc that’s (Introduction to hyperbolic geometry) The Poincar?e disk model for hyperbolic geometry How do Euclid’s propositions change in hyperbolic geometry? Arclength, lines and circles on the Poincar?e disk Lecture 19: Geometry on the Poincare disk.
Other articles where Poincare disk model is discussed: non-Euclidean geometry: Hyperbolic geometry: In the Poincare disk model (see figure, top right), the hyperbolic surface is mapped to the interior of a circular disk, with hyperbolic geodesics mapping to circular arcs (or diameters) in the disk that meet