Geometric Properties of Conics: Ellipses and Their Applications

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Dandelin Theorem: Ellipse Construction

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

Conic Sections: Ellipse, Parabola, Hyperbola

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

Ellipses and Curves in Geometry

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

Hyperboloid Surfaces: Sections and Developability

Delves into the properties of hyperboloid surfaces and their sections, emphasizing developability and curvature.

Conic Synthesis in the Plane

Explores the synthesis of conic sections in the plane, covering eccentricity ratios and parametric equations.

Approximation of Ellipses by Ovals

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

Conic Sections: Planar Curves

Explores conic sections, such as ellipses, hyperbolas, and parabolas, focusing on their geometric and algebraic properties and practical applications.

Geometry: Instrument Epicycle

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

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Conic Sections: Determining Parameters

Explores the determination of conic section parameters and the laws of Kepler in celestial mechanics.