Lectures related to 2D Case: Polynomial Encroaching

Explores the definitions and symmetries of regular polyhedra, shedding light on ancient geometry and modern mathematical formalization.

Covers proper and cast shadows in descriptive geometry with practical examples and exercises.

Explores harmonic ratio in geometry, covering bisectors, harmonic segments, polyhedra, spatial curves, and historical perspectives.

Explores the historical background and significance of symmetries in regular polyhedra, shedding new light on Euclid's Elements.

Explores the properties of regular polyhedra, their symmetries, generation, and historical misconceptions.

Demonstrates the process of including beams and correcting orientations for complex configurations.

Explores symmetry in modern geometry, emphasizing reflections, rotations, and practical applications in computer-aided design.

Explores basic solutions in linear constraints and the equivalence with vertices.

Covers the concepts of faces, facets, and vertices in polyhedra, exploring minimal faces and inequalities.

Explores extreme points, vertices, and basic feasible solutions in polyhedra, emphasizing their properties and construction.

Explores convex polyhedra, linear programs, and their optimization importance.

Explores the definitions and symmetries of regular polyhedra, focusing on the five known convex regular polyhedra from ancient times.

Explores separating hyperplanes for two sets X and Y, discussing conditions for separation and implications of convexity.

Covers the theory of linear and integer programming, focusing on the integer hull and rational polyhedra.

Covers the basics of linear optimization, including equations, polyhedrons, feasible directions, and optimal solutions.

Explores integer programs, nonconvex optimization, constraints, and geometric aspects of linear programming for optimal solutions.

Covers an overview of convex optimization, affine sets, polyhedra, ellipsoids, and convex functions.