Geometric Curve Reparameterization

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Kinematic Quantities and Linear Mass Density

Discusses kinematic quantities and linear mass density in examples of metal wires.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Mechanics of Kirchhoff Rods I

Covers the mechanics of slender structures, focusing on exact kinematics and equilibrium equations of rods.

Differential Geometry: Parametric Curves & Surfaces

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

Spatial Curves: Singularities and Mechanisms

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

Curves in Space: Parametric Equations and Surfaces

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

Arc Length Approximation

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

Intrinsic Geometry of Regular Surfaces

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

Curvature and Osculating Circle

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.