Lectures related to Geometry of Surfaces in R²

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

Ruled Surfaces: Generators and Applications

Explores ruled surfaces, surfaces generated by moving lines in space, including cones, cylinders, and hyperboloids, with applications in architecture.

Curvature and Osculating Circle

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

Introduction to Conic Sections in Space

Covers the introduction to conic sections in space, focusing on ellipses and their properties.

Descriptive Geometry: Cones and Cylinders

Explains the definitions of cones and cylinders as ruled surfaces and how to find tangent planes to them.

Geometric Principles in Architecture: Hyperboloids and Paraboloids

Discusses geometric principles in architecture, focusing on hyperboloids and paraboloids and their applications in design and structural engineering.

Conicity in Modeling

Explores conicity in modeling, addressing challenges at corners and simplifying geometry through the imposition of conicity at vertices.

Homotheties and Translations

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