Lectures related to Theorem of Three Perpendiculars, Shadow of a Point

Mediatrix and Bisector

Explores the mediatrix and bisector properties in right-angled triangles through proofs and constructions.

Relative Positions in Space

Covers the precise description of the relative positioning of objects in space.

Elliptical Arch Construction

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

Vectors: Definitions and Operations

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

Stereographic Projection: Sphere Parameterization

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

Curvature and Osculating Circle

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

Angle at the Center & Power of a Point

Explores the angle at the center and the power of a point relative to a circle, demonstrating key theorems and geometric concepts.

Geometry: Euclidean Elements & Vitruvius

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

Conics in the Plane: Uniform Description of 3 Conics

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

Orthogonality and Least Squares Method

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

Euclidean Geometry: Operations and Constructions

Covers the fundamental operations and constructions in Euclidean geometry, focusing on algebraic interpretations and ruler-and-compass constructions.

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.

Capacitor and Self-Heating in a Wire

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

Distance Between Two Lines

Covers the concept of finding the distance between two lines in a plane.

Geometric Transformations: Meanings and Applications

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

Elementary Operations in Geometry

Explores elementary operations in geometry, including addition, subtraction, multiplication, and division of segments and angles.

Homotheties and Translations

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

Geometry: Instrument Epicycle

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

Isometries & Orientation in Modern Geometry

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Vector Equations and Normal Equations

Explores vector and normal equations, covering lines, intersections, and distances in 2D and 3D geometry.