Lectures related to Apollonius of Perga

General Conics: Symmetry and Elimination

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

General Conics and Motor Blocks

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

Homogeneous Coordinates and Conics

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

Conics in the Plane: Uniform Description of 3 Conics

Explores the construction and properties of parabolas, ellipses, and hyperbolas in the plane.

General Conics and Homogeneous Coordinates

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

Conic Sections: Ellipse, Parabola, Hyperbola

Explores conic sections like ellipse, parabola, and hyperbola, their properties, constructions, and perspectives in 2D and 3D spaces.

Dandelin Theorem: Ellipse Construction

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

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.

Geometry: Passage to Space

Explores the transition from 2D to 3D geometry, covering conical sections, spatial curves, and equivalent shapes.

General Conics: Ellipse and Hyperbola

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

Conic Sections: Equivalence and Intersection

Delves into the historical context and mathematical properties of conic sections like parabolas, ellipses, and hyperbolas.

Conical Sections: Apollonius

Explores conical sections according to Apollonius, focusing on visual cones and unique shapes.

Quadratic Forms: Definitions, Examples

Covers the definition of quadratic forms in R^n with examples in R^2 and R^3.

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.

Canonical Analysis: Quadratic Geometry

Explores canonical analysis of quadratic functions to identify conic shapes in planes.

Conic Sections & Gnomonics

Explores the historical use of conic sections and gnomonics in ancient sundials and astronomical instruments.

Approximation of Ellipses by Ovals

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

Ellipses and Conics

Explores ellipses, conic sections, Kepler's laws, and geometric reconstruction in architectural modeling.

Conics in Space: Exam Review and Parametric Equations

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

Construction of Ovals: From Roman Amphitheatres to Modern Architecture

Explores the historical construction methods of ovals, from Roman amphitheatres to modern architecture, including the use of symmetrical double tangency.