Concept

Peano curve

Related lectures (19)

Discusses limit cycles, equilibrium points, arbitrary curves, abstract plane, and numbering of points.

Covers the calculation of curvilinear integrals for a continuous function in R^n and the interpretation of the integral as the sum of small segments along a curve.

Gaussian Curvature and Geodesics

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Curve Length

Explores the concept of curve length and its geometric properties.

Curves in Space: Parametric Equations and Surfaces

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Curves: differentiability and smoothness

Explores the differentiability and smoothness of curves in R², covering criteria, singularity points, and length.

Fractal Dimension: Understanding Complex Geometric Structures

Explores fractal dimension, calculating values analytically and providing practical examples in computer graphics.

Curves and Isometries

Explores curves, isometries, Bezier curves, and the Frenet coordinate system.

Hydration: Aluminate Hydrates

Delves into aluminate hydrates in cement chemistry, discussing ettringite, AFm phases, decomposition, solid solutions, limestone effect, and hydrogarnets.

Manifolds and Tangent Space

Introduces manifolds, charts, atlases, tangent space, tensors, and the metric in curved spaces.

Geometric Quantities in Parameterized Curves

Explores parameterized curves, regularity, and geometric quantities like the carbide vector and curvature.

Riemannian distance, geodesically convex sets

Covers the structure of Riemannian manifolds, geodesic convexity, and the Riemannian distance function.

Curve Length and Function Definition

Explores curve length, function definition, continuity, derivatives, integrals, and graphical representations of functions in two variables.

Surface of Revolution

Explains the parametric equations of surfaces of revolution generated by curves in space.

Curves: Parameterized Curves and Tangent Vectors

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

General Covariance in Gravity

Explores general covariance in gravity, covering equations, curvature tensor, and static gravity field.

The Richardson Cascade

Explores the Richardson cascade, energy cascade, eddy generations, scale separation, Reynolds numbers, and energy contributions.

Spatial Curves: Singularities and Mechanisms

Explores spatial curves, singularities, and mechanisms, analyzing their geometric properties and applications.

General Covariance in Gravitational Field

Explores general covariance, Riemann tensor, Bianchi identities, and Einstein tensor in gravitational field.