Concept

Arc length

Related lectures (30)

Explores arc length calculation for curves and polygons inscribed in circles using trigonometry and parametric equations.

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.

Integral Applications: Arc Length

Explores finding circle circumference and parametric curve arc length using integration and derivatives.

Gaussian Curvature and Geodesics

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

Triangle Inequality Theorem

Covers the Triangle Inequality Theorem in triangles, showing side length relationships.

Parametrization by Arc Length

Covers parametrization by arc length for representing curves with continuous differentiability.

Intrinsic Geometry of Regular Surfaces

Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.

Stéréotomie: Modeling Stone Structures

Covers the modeling of stone structures, collaborative work, and systematic document management for student projects.

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Differential Geometry: Curves

Explores the geometry of parametric curves, covering tangent vectors, curvature, and curve smoothing techniques.

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Bounding the Poisson bracket invariant on surfaces

Covers the concept of bounding the Poisson bracket invariant on surfaces, exploring joint work with A. Logunov and S. Tanny.

Curvilinear Integrals

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.

Arc Length: Circle Circumference and Parametric Curves

Covers circle circumference calculation and parametric curve arc length determination.

Curves in Space

Explores approximating curves in space and preparing for an upcoming exam.

Derivatives and Functions: Definitions and Interpretations

Covers the definition of derivative functions and their interpretation, focusing on differentiability, velocity, and curve lengths.

Calculus Applications: Lengths and Surfaces of Revolution

Discusses the applications of calculus in calculating lengths and surfaces of revolution, emphasizing integral calculus and geometric interpretations.

Curvilinear Integrals and Green's Theorem

Introduces curvilinear integrals, parameterization, and Green's Theorem for conservative fields.

Compression: Prefix-Free Codes

Explains prefix-free codes for efficient data compression and the significance of uniquely decodable codes.