Lectures related to Analytical Geometry: Circles and Planes

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

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.

Differential Geometry: Parametric Curves & Surfaces

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

Surface of Revolution

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

Introduction to Conic Sections in Space

Covers the introduction to conic sections in space, focusing on ellipses and their properties.

Conicity in Modeling

Explores conicity in modeling, addressing challenges at corners and simplifying geometry through the imposition of conicity at vertices.

Analytical Geometry: Cartesian Equations

Covers Cartesian equations in analytical geometry, focusing on encoding line directions and unique equations.

Analytical Geometry: Relative Positions in Space

Explores relative positions of lines in space, discussing parallel, secant, and confused lines.