Lectures related to Geometry I: Euclidean Propositions & Symmetry

Geometry: Euclidean Elements & Vitruvius

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

Delves into modern geometry, covering transformations, isometries, and symmetries.

Geometry: Introduction to Architectural Geometry

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

Orthogonal Projections: Symmetry and Matrices

Explores orthogonal projections, symmetry of matrices, and their applications.

Symmetry & Boundary Conditions

Explores symmetry and boundary conditions in finite element models, emphasizing the importance of maintaining symmetry for accurate modeling.

Geometry: Inaugural Proposition

Explores the Inaugural Proposition of Euclid's Elements and practical exercises using TopSolid software.

Regular Polyhedra: Symmetries & Generation

Explores the properties of regular polyhedra, their symmetries, generation, and historical misconceptions.

Circle Orthogonal & Poincaré Disk

Covers circle orthogonal and Poincaré disk concepts in geometry.

Geometry: Modern Interpretation of Symmetry

Introduces a new online format for the geometry course, emphasizing the study of isometries and the modern interpretation of symmetry.

Symmetry in Geometry

Explores modern symmetry in geometry, covering transformations, isometries, orientations, and practical applications.

Affinity and Ellipses in Descriptive Geometry

Explores affinity in geometry, segment construction, ellipses, and circle projections.

Elliptical Arch Construction

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

Geometry: Inaugural Proposition

Explores the common inaugural proposition of Euclid and Vitruvius, focusing on commensurability and geometric figure construction.

Power of a Point in Geometry

Explores the power of a point outside a circle and its practical applications.

Introduction to Non-Euclidean Geometry

Explores non-Euclidean geometries, hyperbolic and spherical, challenging the traditional Euclidean geometry with implications for modern mathematics.

Inversion & Family of Orthogonal Circles

Explores inversion, orthogonal circles, unique projective, and non-constructible figures in geometry.

Geometric Transformations: Meanings and Applications

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

Conics in the Plane: Uniform Description of 3 Conics

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

Geometry: Euclidean Propositions and Architectural Foundations

Explores Euclid's first proposition and its architectural implications, emphasizing the enduring relevance of classical geometric principles in contemporary architectural practice.

Live Written Correction: Centroids and Distributed Forces

Covers live written corrections for exercises on centroids and distributed forces in structural mechanics.