Lecture

Conics in Space: Exam Review and Parametric Equations

Related lectures (28)

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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.

Conics in Geometry: Ellipses, Parabolas, and Hyperbolas

Provides an overview of conics, including ellipses, parabolas, and hyperbolas, focusing on their properties, equations, and applications in geometry and physics.

Geometric Areas: Integrals and Regions

Covers the calculation of areas using integrals for geometric regions defined by curves and parametric equations.

Geometric Properties of Ellipses and Their Applications

Explores the geometric properties of ellipses, their parametric equations, and applications in architecture and design.

Conic Synthesis in the Plane

Explores the synthesis of conic sections in the plane, covering eccentricity ratios and parametric equations.

Approximation of Ellipses by Ovals

Explores the historical development of approximating ellipses with ovals and the challenges in machining trajectories.

Differential Geometry: Parametric Curves & Surfaces

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

Parametric Curves: Envelope and Caustics

Explores parametric curves, focusing on finding envelopes and caustics.

Curvature and Inflection Points

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Geometry: Opening of the Course on February 25

Covers the synthesis of results from the first semester, focusing on flat curves, spatial curves, surfaces, and projections.

Geometrical Aspects of Differential Operators

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