Lectures related to Geometric Means: Ancient Theories and Modern Applications

Symmetry in Modern Space

Explores the classification and practical applications of symmetries in 3D space, emphasizing user-driven determination of object symmetries.

Geometric Transformations: Meanings and Applications

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

Geometry II: Modern Geometric Transformations

Explores modern geometric transformations and invariances, focusing on projective geometry and historical developments.

The 3 Branches: Geometric Means & Constructibility

Delves into ancient geometric means, transformations, and projective geometry's birapports.

Harmonic Mean: Geometric Projective Geometry

Explores the harmonic mean in visual arts and projective geometry, discussing historical context and invariance properties.

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.

Euclidean Geometry: Operations and Constructions

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

Geometry: Introduction to Architectural Geometry

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

Geometry: Introduction to Euclidean Elements

Explores the historical evolution of geometric instruments and the transition to modern CAD software for architectural design.

Average Growth Rates Calculation

Explains how to calculate average growth rates using arithmetic mean, geometric mean, and linear trend analysis.

ECDF and Quantiles

Covers ECDF, quantiles, mean, median, and box plots for dataset analysis.

Geometric Means: Simple, Double, and Harmonic

Explores the construction and mathematical properties of simple, double, and harmonic geometric means using ruler and compass.

Geometric Transformations: Projective Geometry Fundamentals

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

Attenuation Correction

Explores the fundamentals of attenuation correction in biomedical imaging and simplifies the process using the geometric mean at 180°.

Calculating Growth Rates

Explores the calculation of growth rates, average GDP growth, and environmental footprint changes.

Angle at the Center & Power of a Point

Explores the angle at the center and the power of a point relative to a circle, demonstrating key theorems and geometric concepts.

Symmetry in Geometry

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

Geometric Operations: Inversion & Orthogonal Circles

Explores geometric operations like inversion, orthogonal circles, and cube duplication, emphasizing historical significance and modern construction methods.

Geometric Projections: Historical Perspectives and Applications

Explores the evolution of projective geometry and its applications in architectural representation.

Geometric Meanings: Euclidean Division and Divine Proportion

Explores the historical and mathematical significance of Euclidean Division and the Divine Proportion in geometry and art.