Lectures related to Geometric Meanings: Euclidean Division and Divine Proportion

Geometry: Euclidean Elements & Vitruvius

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

Explores the historical and mathematical significance of duplicating the cube and its geometric implications in ancient times.

Introduction to Real Numbers and Their Properties

Introduces real numbers, their properties, and their significance in analysis.

Geometric Properties of Ellipses and Their Applications

Explores the geometric properties of ellipses, their parametric equations, and applications in architecture and design.

Conic Sections: Equivalence and Intersection

Delves into the historical context and mathematical properties of conic sections like parabolas, ellipses, and hyperbolas.

Geometric Means: Ancient Theories and Modern Applications

Delves into ancient geometric means and their modern applications in geometry.

Triangle Inequality Theorem

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

Introduction to DEMR

Introduces the concept of Division in Extreme and Mean Ratio (DEMR) and its historical significance in geometry.

Geometric Transformations: Meanings and Applications

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

Mathematics: Cylinders and Parametrizations

Discusses the mathematical concepts of cylinders and their parametrizations, including surface area, volume, and related exercises.

Division in Extreme and Mean Ratio: DEMR

Explores Division in Extreme and Mean Ratio (DEMR) for geometric constructions and its historical significance in art and architecture.

Introduction to Analysis

Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.

Injective Functions: Properties and Examples

Covers the properties of injective functions and demonstrates their proofs through examples and visual aids.

Hyperboloid Surfaces: Sections and Developability

Delves into the properties of hyperboloid surfaces and their sections, emphasizing developability and curvature.

Homotheties and Translations

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

Regular Polyhedra in Euclidean Geometry

Explores the historical background and properties of regular polyhedra in Euclidean geometry, including the construction of perfect even numbers and the proportionality of arcs and angles.

Geometric Transformations: Projective Geometry Fundamentals

Covers the fundamentals of projective geometry and its applications in architecture.

Regular Polyhedra: Symmetries & Generation

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