Osculating circle

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Discusses parametric equations, eccentricity, and ellipse tangents, including horizontal and vertical tangents.

Explores the properties and sections of a sphere, including symmetry, tangent planes, and circle projections.

Explores the connection between hyperbolic and trigonometric functions through circles and hyperbolas.

Explores the properties and equations of conic sections, emphasizing geometric interpretations and special characteristics.

Explores the concept of curve length and its geometric properties.

Covers curves in space, including singularities, Frenet frame, and development curves.

Introduces the Limaçon de Pascal, a parametric curve with unique properties.

Introduces the Limaçon de Pascal, a curve described by a moving point on a circle.

Covers the concept of parametrized curves in 2D and their properties.

Explores normal acceleration, spatial rotations, vector rotation, and angular speed concepts in physics.