Lectures related to Curves in the Oriented Plane

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

Covers the mechanics of slender structures, focusing on exact kinematics and equilibrium equations of rods.

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

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Covers geodesic curves parameterized at constant speed to minimize distances between points.

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

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

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

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

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

Explores parameterized curves, regularity, and geometric quantities like the carbide vector and curvature.

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

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

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Explores the Frenet-Serret formulas for curvature and torsion in three-dimensional space.

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

Covers linear independence, bases, and coordinate systems with examples and theorems.