Concept

Hyperbolic geometry

Related lectures (28)

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.

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.

Hyperboloid Surfaces: Sections and Developability

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

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.

Homotheties and Translations

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

Elliptical Arch Construction

Explores the construction of elliptical arches using a single ellipse arc.

Symmetry in Modern Geometry

Delves into modern geometry, covering transformations, isometries, and symmetries.

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.

Geometry: Menaeus de Vitruve

Explores conical and gnomonic curves, celestial representations, and solar paths through sketches and modeling tools.

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.

Conics in the Plane: Uniform Description of 3 Conics

Explores the construction and properties of parabolas, ellipses, and hyperbolas in the plane.

IMesh and iConc Tutorial

Covers the tutorial for iMesh and iConc, focusing on creating Finite Element Mesh for concrete structures.

Vectors: Definitions and Operations

Introduces vector definitions, displacement, addition, and applications in geometry.