Lectures related to Orthonormal Basis in 3D Space

Orthogonality and Least Squares Method

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

Conformity and Compliancy in Geometry

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

Vectors: Definitions and Operations

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

Conics in the Plane: Uniform Description of 3 Conics

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

Analytical Study of Plan: Points, Lines

Covers the analytical study of the plan, focusing on points and lines.

Homotheties and Translations

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

Scalar Products in 2D and 3D Geometry

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

Embedding Space: AdS and Euclidean Geometry

Covers the concept of embedding space for AdS and Euclidean geometry, discussing AdS isometries and Euclidean Ads.

Elliptical Arch Construction

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

The Universe: Describing Size, Mass-Energy, Geometry, and Evolution

Explores the Universe's size, mass-energy, geometry, and evolution, including redshift effects and accelerating expansion.

Geometry: Euclidean Elements & Vitruvius

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

Hilbert Space: Geometry, Bases

Explores Hilbert space, scalar product, geometry, bases, complex functions, and quantum mechanics applications.

Orthogonality and Scalar Product

Explores orthogonality, scalar product, and orthonormal bases in vector spaces.

Geometry: Instrument Epicycle

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

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.

Euclidean Spaces: Properties and Concepts

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Euclidean Geometry: Operations and Constructions

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

Vectors: Coordinate Calculations

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

Capacitor and Self-Heating in a Wire

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

Hilbert Spaces: Orthonormal Systems

Explores Hilbert spaces, orthonormal systems, and the Bessel inequality, emphasizing their properties and significance.