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Concept

Hyperbolic geometry

Related lectures (28)

Hyperbolic Geometry

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

Introduction to Non-Euclidean Geometry

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

Introduction to Euclidean Elements

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

Inversion & Orthogonal Circles

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

Conformal Maps and Hyperbolic Geometry

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

Euclidean Geometry: Operations and Constructions

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

Circle Orthogonal & Poincaré Disk

Covers circle orthogonal and Poincaré disk concepts in geometry.

Introduction to Euclidean Elements

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

Euclidean Geometry Fundamentals

Introduces the fundamentals of Euclidean geometry, covering equilateral triangles, symmetries, radical axes, and ancient architectural figures.

Dynamics of Singular Riemann Surface Foliations

Explores the dynamics of singular Riemann surface foliations and their intricate behavior.

Capacitor and Self-Heating in a Wire

Covers the simulation of a capacitor and self-heating in a wire using Comsol.

Steric Factors in Organic Chemistry

Explores diastereotopic epochs, vi-disconnections, steric factors, and the chelete effect in organic chemistry, along with the protection of alcohols and types of ethers.

Introduction to Euclidean Geometry

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

Main Lines of a Plane: Sketch and Properties

Covers defining a plane by its traces and determining its properties.

Resonances for Hyperbolic Cylinders

On hyperbolic cylinder resonances explores Schottky groups and transfer operators.

Stereographic Projection and Metric Tensors

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

Symmetry in Geometry

Explores modern symmetry in geometry, covering transformations, isometries, orientations, and practical applications.

Barycenters: Examples

Covers examples of barycenters and expressing points as barycenters of given points.

Hyperboloid Surfaces: Sections and Developability Log in to Mediaspace to watch this video

Delves into the properties of hyperboloid surfaces and their sections, emphasizing developability and curvature.

Homotheties and Translations Log in to Mediaspace to watch this video

Explores homotheties and translations in geometry, focusing on preserving alignment and distances.