Concept

Hyperbolic triangle

Related lectures (17)

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Explores non-Euclidean geometries, hyperbolic and spherical, challenging the traditional Euclidean geometry with implications for modern mathematics.

Pythagorean Theorem

Introduces the Pythagorean theorem, explaining its geometric significance and applications in calculating areas.

Stereographic Projection and Metric Tensors

Explores stereographic projection and metric tensors on hyperbolic planes, emphasizing isometry and conforming models.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Conformal Maps and Hyperbolic Geometry

Explores conformal maps, hyperbolic geometry, and isometric properties of disks.

Inversion & Orthogonal Circles

Explores the concept of inversion relative to a circle and its applications in constructing orthogonal circles.

Mediatrix and Bisector

Explores the mediatrix and bisector properties in right-angled triangles through proofs and constructions.

Introduction to Euclidean Elements

Introduces Euclidean elements, explores infinity uniqueness, parallel lines, and different geometries like Euclidean, hyperbolic, and spherical.

Introduction to Euclidean Geometry

Introduces the fundamental concepts of Euclidean geometry, exploring postulates, parallel lines, and non-Euclidean geometries.

Parallel Flow Instability

Explores parallel flow instability, velocity ratio effect, and solving the Rayleigh equation.

Euclidean Geometry: Operations and Constructions

Covers the fundamental operations and constructions in Euclidean geometry, focusing on algebraic interpretations and ruler-and-compass constructions.

The Discriminant: Symmetry and Orbits

Explores the discriminant's role in equations, symmetry, and orbits in mathematical spaces.

Non-Euclidean Geometries

Explores non-Euclidean geometries, including hyperbolic geometry and the tractricoid model, challenging Euclidean principles and introducing projective geometry.

Unit Tangent Bundle of Hyperbolic Spaces

Covers the unit tangent bundle of hyperbolic spaces and geodesic flows.

Parallel Flow Concepts: Mixing Layers

Explores parallel flow concepts, focusing on mixing layers, dispersion relations, and stability analysis through eigenvalues.

Introduction to Euclidean Elements

Introduces the 5th postulate in Euclidean geometry and explores non-Euclidean geometries and their implications.