Delves into the geometric principles of Gothic architecture, focusing on surface curvature and stereotomy techniques.
Covers the topology of Riemann surfaces, focusing on orientation and orientability.
Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.
Explores the definitions and symmetries of regular polyhedra, focusing on the five known convex regular polyhedra from ancient times.
Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.
Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.
Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.
Explains the parametric equations of surfaces of revolution generated by curves in space.
Explores the historical development of approximating ellipses with ovals and the challenges in machining trajectories.
