Cycloid

Formal sciences
Mathematics
Geometry
Differential geometry

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Related lectures (12)

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

Quadrature & Trisection: Geometric Constructions

Explores the historical and mathematical aspects of quadrature and trisection in geometry, including the challenges faced by ancient mathematicians.

Curvature and Osculating Circle

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

Elastic Collisions and Rotational Motion

Explores elastic collisions, rolling cylinders, and ballistic pendulums.

Fourier Series Interpretation

Explores the interpretation of Fourier series from basic to complex signals, demonstrating the concept through animations and explaining the relationship between sine waves and circles.

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.

Variational Methods: Shortest Time Path Problem

Covers variational methods to find the shortest time path for a particle under gravity.

Minimization Principle: Experiments

Explores experimental examples where different shapes minimize specific properties.

Magnetic Pendulum

Explores the design and simulation of a magnetic pendulum model.

Differential Geometry: Curves

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

Energy: Examples, Summary, CMS

Covers examples of energy, efficiency, and conservation of mechanical energy, with exercises on kinetic energy and power.

Differential Geometry: Parametric Curves & Surfaces

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

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