Lectures related to Geometry and Complex Numbers in R²

Covers vector spaces in R2 and R3, including planes and lines.

Geometry and Complex Numbers: Circles in the Complex Plane

Explores equations and properties of circles in the complex plane.

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

Additional Definitions and Basic Properties MOOC: Analysis I MOOC: Analysis I (part 2) : Introduction to complex numbers

Covers additional definitions and basic properties of complex numbers, including conjugate and absolute value.

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.

Scalar Products in 2D and 3D Geometry MOOC: Linear Algebra (Part 3)

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

Capacitor and Self-Heating in a Wire

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

Introduction to Euclidean Elements

Introduces Euclidean elements, explores infinity uniqueness, parallel lines, and different geometries like Euclidean, hyperbolic, and spherical.

Geometric Transformations: Meanings and Applications

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

Geometry: Introduction to Architectural Geometry

Explores the historical and practical applications of geometry in architecture, emphasizing key geometric principles in architectural design.

Hilbert Spaces: Orthonormal Systems Log in to Mediaspace to watch this video

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

Orthogonality and Least Squares Method Log in to Mediaspace to watch this video

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

Euclidean Spaces: Properties and Concepts Log in to Mediaspace to watch this video

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

Vectors: Definitions and Operations Log in to Mediaspace to watch this video

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

Complex Numbers: Applications and Representations Log in to Mediaspace to watch this video

Explores the origin, applications, and representations of complex numbers in crystallography and materials science, including their graphical, polar, and exponential forms.

Vector Operations and Geometry Log in to Mediaspace to watch this video

Covers mathematical concepts related to vector operations and geometry, including scalar product and vector norms.

Geometry: Instrument Epicycle Log in to Mediaspace to watch this video

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

Elliptical Arch Construction Log in to Mediaspace to watch this video

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

Geometry: Course Overview & 5 Regular Polyhedra Log in to Mediaspace to watch this video

Explores geometry basics, 5 regular polyhedra construction, and their link to ancient physics and planets.

Geometry: Geometric Computing Log in to Mediaspace to watch this video

Covers fundamental concepts in geometric computing, exploring stability, vector spaces, barycentric coordinates, and triangle meshes.