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Geometry: Hyperbolic space - the upper half-space and Poincaré disk models. 2nd Year Student Lecture

Professor of Mathematics

47:32·2026·undergraduate level·Standalone Lecture

This lecture introduces two fundamental models of hyperbolic space: the upper half-plane and the Poincaré disk. It rigorously examines their intrinsic symmetries, geodesic paths, and the deep connection to Möbius transformations in complex analysis.

This second lecture from Jason's geometry course, will describe two more ways to view hyperbolic space: on the upper-half of the plane and on the unit disk. In both cases we will describe the symmetries of the hyperbolic model and its geodesics (the shortest paths between points), and see connections to Möbius transformations in complex analysis.

You can watch the first lecture here: https://youtu.be/m_5Jlquo0W4

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