Lectures related to Homogeneous Coordinates and Curves

Homogeneous Coordinates and Conics

Explores homogeneous coordinates, conics like ellipses, hyperbolas, and parabolas, and rewriting equations.

Homogeneous Coordinates: Ellipse and Hyperbola

Explores homogeneous coordinates, emphasizing ellipse and hyperbola properties.

Conic Sections: Ellipse and Hyperbola

Explores properties of conic sections, center, equations, and coordinate transformations.

Analytical Geometry: Hyperbola and Ellipse

Covers the concepts of the hyperbola and ellipse in analytical geometry.

General Conics and Homogeneous Coordinates

Covers general conics, homogeneous coordinates, conic recognition, and matrix decomposition.

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.

General Conics and Motor Blocks

Explores general conics, motor blocks, and homo coordinates in matrix decomposition and coefficient calculations.

Conic Sections: Basics and Properties

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

General Conics: Symmetry and Elimination

Covers the concepts of mixed product, cross product, homo coordinates, and general conics.

Geometry of Hyperbolas and Ellipses

Explores the construction of hyperbolas and ellipses, along with geometry properties and exercises on circles.

Surface of Revolution

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

Curvature and Osculating Circle

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

Geometrical Aspects of Differential Operators

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

Conic Sections: Definitions and Equations

Explores the definitions and equations of conic sections, including parabolas, ellipses, and hyperbolas, with practical geometric applications.

Geometry: Ellipse and Hyperbola

Explores the properties of ellipses, hyperbolas, circles, and products in geometry.

General Conics: Ellipse and Hyperbola

Explores general conics, emphasizing ellipses and hyperbolas, discussing passage matrix, cross product, and eigenvalues.

Curves with Poritsky Property and Liouville Nets

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

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Analytical Geometry: Conic Sections

Covers the properties and equations of conic sections.

Curves and Surfaces

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