Conics in Space: Exam Review and Parametric Equations

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Curvature and Osculating Circle

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

Surfaces in Space

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Dandelin Theorem: Ellipse Construction

Explores ellipse construction using the Dandelin theorem and properties of conics in space.

Curves in Space: Parametric Equations and Surfaces

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

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Arc Length Approximation

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

Surface of Revolution

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

Curves with Poritsky Property and Liouville Nets

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

Parametric Equations: Benchmark of Observation

Explores parametric equations and their dependence on the choice of observation benchmarks.

Curves and Surfaces

Covers the representation of plane curves and the nature of obtained curves.