Curves in Space: Singularities and Developments

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Curvature and Osculating Circle

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

Curves and Isometries

Explores curves, isometries, Bezier curves, and the Frenet coordinate system.

Singularities of Curves in Geometry

Explores singularities in curves, including inflection points and points of reversal, and discusses the evolution of torsion along curves.

Curves in Space: Parametric Equations and Surfaces

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

Curves with Poritsky Property and Liouville Nets

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

Surfaces in Space

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Geometrical Aspects of Differential Operators

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

Unclosed Curves Integrals

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

Regular Curves and Constant Speed

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

Gothic Surfaces: Curvature, Development, and Stereotomy

Delves into the geometric principles of Gothic architecture, focusing on surface curvature and stereotomy techniques.