Surface Geometry: Geodesics and Surface Area

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Ellipses and Conics

Explores ellipses, conic sections, Kepler's laws, and geometric reconstruction in architectural modeling.

Calculus Applications: Lengths and Surfaces of Revolution

Discusses the applications of calculus in calculating lengths and surfaces of revolution, emphasizing integral calculus and geometric interpretations.

Surfaces with Variable Curvature

Explores surfaces with variable curvature, discussing their construction and properties.

Angle Calculation on Regular Surfaces

Covers the calculation of angles between curves on regular surfaces and the concept of curvilinear abscissa.

Real Surfaces: Defects and Reconstructions

Explores the difference between ideal and real surfaces, defects, and surface reconstructions.

Geometry: Euclidean Elements & Vitruvius

Explores Euclid's first proposition, ancient symmetria, and Vitruvius' architectural figures.

Homotheties and Translations

Explores homotheties and translations in geometry, focusing on preserving alignment and distances.

Geometry: Menaeus de Vitruve

Explores conical and gnomonic curves, celestial representations, and solar paths through sketches and modeling tools.

Curves with Poritsky Property and Liouville Nets

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

Symmetry in Modern Geometry

Delves into modern geometry, covering transformations, isometries, and symmetries.