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Related lectures (24)

Vectors: Definitions and Operations

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

Geometry: Euclidean Elements & Vitruvius

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

Orthogonality and Least Squares Method

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

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Plan Separation

Explores the axiom of separating the plane into two half-planes and the concept of interior points.

Geometric Transformations: Meanings and Applications

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

Linear Similarities and Similitudes

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

Elliptical Arch Construction

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

Vectors and Kinematics

Introduces vectors in a solid reference frame and explains the importance of determinants in interpreting vector products and coordinate changes.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

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.

Homotheties and Translations

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

Capacitor and Self-Heating in a Wire

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

Scalar Products in 2D and 3D Geometry

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

Geometry and Meshing

Covers the basics of geometry modeling and meshing for numerical flow simulation, including mesh quality metrics and different meshing algorithms.

Triangle Inequality Theorem

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

Euclidean Geometry: Operations and Constructions

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