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Lecture
Homogeneous Coordinates and Curves
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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.