Concept

Cubic plane curve

Related lectures (25)

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

Incidence Geometry & Elliptic Curves

Explores the Cayley-Bacharach theorem in incidence geometry and introduces elliptic curves with a commutative law.

Perspective of a Sphere & a Circle

Explores conical sections, plane curves, and the perspective of a sphere and a circle.

Elliptic Curves: Singular Points and Group Law

Explores singular points, the group law, and the ambiguity in defining the sum of a point with itself on elliptic curves.

Projective Geometry: Tangent Lines

Discusses the correction of tangent lines and projective plane curves, exploring topological applications and curve structure.

Epicyclic Curves: Modeling Instruments for Plane Curves

Explores modeling instruments for generating plane epicyclic curves, including circles and ellipses, and their spatial counterparts.

Projective Plane Curves

Introduces projective plane curves, degrees, components, multiplicities, intersection numbers, tangents, and multiple points, culminating in the statement of Bézout's theorem and its consequences.

Intersection Numbers: Properties and Computation

Explores intersection numbers of plane curves, their properties, and computation methods.

DVR and Irreducible Plane Curves

Explores Discrete Valuation Rings and their role in irreducible plane curves.

Geometry: Course Overview & 5 Regular Polyhedra

Explores geometry basics, 5 regular polyhedra construction, and their link to ancient physics and planets.

Curvature and Osculating Circle

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

Conics in Space: Exam Review and Parametric Equations

Explores the provisional course agenda, conics in space, and parametric equations.

Curves and Surfaces

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

Plane Curves: Singular Points and Multiplicities

Explores plane curves, focusing on singular points, multiplicities, and tangent lines.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Dandelin Theorem: Ellipse Construction

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

Irreducible Algebraic Sets

Explores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.

Frenet-Serret Formulas: Curvature and Torsion

Explores the Frenet-Serret formulas for curvature and torsion in three-dimensional space.

Affine Varieties and Hypersurfaces

Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.

Bézout's Theorem and Cayley-Bacharach

Explores Bézout's theorem and Cayley-Bacharach, discussing intersection multiplicities and linear combinations in projective geometry.