Curvature and Osculating Circle

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Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

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

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

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

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

Examines geometric singularities in architectural design through the analysis of spatial intersections.

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

Covers the geometric properties of hyperbolic paraboloids and hyperboloids, focusing on their construction and curvature characteristics.

Explores the geometry of parametric curves, covering tangent vectors, curvature, and curve smoothing techniques.

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