Course

MATH-123(b): Geometry

Lectures in this course (35)

Covers basic notions of vector geometry, including scalar product, norm, and projection.

Covers equations and parametrizations of planes, and the formula for rotations.

Covers affine subspaces, lines, planes, intersections, cross product, and distance calculations in vectorial geometry.

Covers the preservation of isometry by rotations and symmetries.

Explores isometries, distinguishing between rotations and reflections, and the preservation of orientation in geometric transformations.

Explores the standard form of isometries in R^n and the preservation of distances.

Explores isometries in R^2 and R^3, focusing on symmetries, rotations, and linear compositions, with a glimpse into the Banach-Tarski paradox.

Explores parameterization of curves, emphasizing continuous settings and accurate curve representation through various examples.

Explores curve parametrization, including setting curves, trace, and direction preservation.

Explains vector functions and the parameterization of curves with examples.

Explores Bezier curves, emphasizing control points and curve regularity.

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

Explores the concept of curve length and its geometric properties.

Explains the curvature oriented change of notes in OneNote for Windows 10.

Explores the concepts of curvature, oriented curvature, and inflection points in regular curves.

Explains vector fields, Frenet frame, and local curve behavior using Frenet-Serret formulas.

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

Covers implicit curves, regular and critical points, convexity, concavity, and inflection points.

Covers the TNB frame and Frenet-Serret formulas for understanding curve behavior.

Explores stereographic projection and sphere parameterization, emphasizing regularity and line independence.