Lectures related to Involutes and Bezier Curves

Curvature and Osculating Circle

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

Curves in Space: Parametric Equations and Surfaces

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Parametric Curves: Basics and Applications

Covers the basics of parametric curves, including straight lines, quadratic curves, Bézier curves, and cubic curves.

Geometric Properties of Ellipses and Their Applications

Explores the geometric properties of ellipses, their parametric equations, and applications in architecture and design.

Arc Length Approximation

Explores arc length calculation for curves and polygons inscribed in circles using trigonometry and parametric equations.

Curves with Poritsky Property and Liouville Nets

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

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.

Surface of Revolution

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

Differential Geometry: Parametric Curves & Surfaces

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

Parametric Curves: Envelope and Caustics

Explores parametric curves, focusing on finding envelopes and caustics.

Tangent Vectors and Bézier Curves

Explains tangent vectors of curves and the construction and applications of Bézier curves in computer graphics.

Envelope of Curves

Explores the concept of envelope of curves within families of lines, including implicit equations, super-ellipses, and curvature.

Topology of Riemann Surfaces

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

Elliptic Curves: Theory and Applications

Covers the theory and applications of elliptic curves in cryptography and number theory.

Parametric Equations: Benchmark of Observation

Explores parametric equations and their dependence on the choice of observation benchmarks.

Bezier Curves: Fundamentals and Applications

Explores the fundamentals and applications of Bezier curves, focusing on their construction, properties, and practical uses in design and modeling.

Introduction to Conic Sections in Space

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

Extended Josephson Junctions: Modeling and Critical Current

Covers the magnetic thickness, short and long junctions, and critical current.

Surfaces in Space

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Parametrized Curves in 2D

Covers the concept of parametrized curves in 2D and their properties.