Ellipse and Circle Tangents

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Curves and Surfaces

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

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.

Conic Sections: Ellipse and Hyperbola

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

General Conics: Ellipse and Hyperbola

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

Descriptive Geometry: Ellipse Projections

Explores ellipse projections, discussing properties, construction methods, and practical examples.

Surface of Revolution

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

Geometric Places: Symmetry and Properties

Covers geometric places, symmetry, alignment, circles, radii, diameters, and more in a plane.

Elliptical Trajectories: Epicyclic System & Instruments

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

Curves with Poritsky Property and Liouville Nets

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