Ellipse: Parametric Equations and Tangents

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Ellipse: Astronomical Evolution to Mathematical Formulation

Explores the transition from geocentric to heliocentric models and the mathematical principles behind elliptical trajectories.

Elliptical Orbits: Examples and Formulas

Covers examples and formulas related to elliptical orbits and how to determine parameters of an elliptical orbit using known points.

Analytical Geometry: Tangents and Circles

Explores Cartesian equations of tangents, vector equations, and rules for doubling and duplication in circles.

Analytical Geometry: Circles and Tangents

Explores circles, tangents, right lines, planes, and vector products in analytical geometry.

Curves with Poritsky Property and Liouville Nets

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

Conics in the Plane: Uniform Description of 3 Conics

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

Parametric Curves: Limaçon de Pascal

Introduces the Limaçon de Pascal, a parametric curve with unique properties.

Parametric Curves: Pascal's Limaçon

Introduces the Limaçon de Pascal, a curve described by a moving point on a circle.

General Conics and Homogeneous Coordinates

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

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.