Lectures related to Epicyclic Curves: Modeling Instruments for Plane Curves

Curves with Poritsky Property and Liouville Nets

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

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

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

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: Instrument Epicycle

Explores the invention of instruments by artists like Albrecht Dürer to draw complex curves and lines not achievable with a ruler.

Regular Curves and Constant Speed

Covers regular curves and constant speed, with examples of circles and helices.

Surfaces in Geometry II

Explores geometric surfaces, rules between shapes, and architectural applications.

Curves and Surfaces

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

Elliptical Trajectories: Epicyclic System & Instruments

Explores elliptical trajectories in the Copernican system and the instruments used to trace them.

Dandelin Theorem: Ellipse Construction

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

Geometry of Hyperbolas and Ellipses

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

Parametrized Curves in 2D

Covers the concept of parametrized curves in 2D and their properties.

Curvature and Inflection Points

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

Analytic Geometry x Hyperbola: Ellipse and Affinity

Covers topics related to analytic geometry, hyperbolas, ellipses, and affinity.

Perspective of a Sphere & a Circle

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

Ellipses and Curves in Geometry

Explores ellipses, curves, and their applications in astronomy and mathematics.

Curves in Space: Parametric Equations and Surfaces

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Approximation of Ellipses by Ovals

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

Geometry: Course Overview & 5 Regular Polyhedra

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

Residue Theorem: Calculating Integrals on Closed Curves

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