Lectures related to Plan Separation

Area: Axioms and Rectangles

Covers the concept of area, axioms, and the area of rectangles.

Linear Similarities and Similitudes

Explores linear similarities and similitudes, demonstrating their properties and applications in geometry.

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Elliptical Arch Construction

Explores the construction of elliptical arches using a single ellipse arc.

Steric Factors in Organic Chemistry

Explores diastereotopic epochs, vi-disconnections, steric factors, and the chelete effect in organic chemistry, along with the protection of alcohols and types of ethers.

Conics in the Plane: Uniform Description of 3 Conics

Explores the construction and properties of parabolas, ellipses, and hyperbolas in the plane.

Vectors: Definitions and Operations

Introduces vector definitions, displacement, addition, and applications in geometry.

Axioms of Connection

Introduces the axioms of connection in Euclidean geometry, emphasizing unique lines and non-collinear points.

Geometric Transformations: Meanings and Applications

Explores geometric transformations, invariant properties, and mean relationships in modern geometry.

Rigidity in Negative Curvature

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Stereographic Projection: Sphere Parameterization

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

Capacitor and Self-Heating in a Wire

Covers the simulation of a capacitor and self-heating in a wire using Comsol.

Geometry: Instrument Epicycle

Explores the invention of instruments by artists like Albrecht Dürer to draw complex curves and lines not achievable with a ruler.

Geometry II: Modern Geometric Transformations

Explores modern geometric transformations and invariances, focusing on projective geometry and historical developments.

Triangle Inequality Theorem

Covers the Triangle Inequality Theorem in triangles, showing side length relationships.

Orthogonality and Least Squares Method

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

Introduction to Euclidean Elements

Introduces the fundamental concepts of Euclidean geometry, focusing on the Elements of Euclid and the logical structure of geometric propositions.

Theorem of Three Perpendiculars, Shadow of a Point

Explains the Theorem of Three Perpendiculars and shadow casting of points on planes.

Homotheties and Translations

Explores homotheties and translations in geometry, focusing on preserving alignment and distances.

Geometry: Euclidean Elements & Vitruvius

Explores Euclid's first proposition, ancient symmetria, and Vitruvius' architectural figures.