Lectures related to Cube Duplication: Geometric Insights

Geometry: Euclidean Elements & Vitruvius

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

Conic Sections: Equivalence and Intersection

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

Geometric Meanings: Euclidean Division and Divine Proportion

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

Geometry: Inaugural Proposition

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

Elliptical Arch Construction

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

Triangle Inequality Theorem

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

Geometric Properties of Ellipses and Their Applications

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

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.

Calculus Applications: Lengths and Surfaces of Revolution

Discusses the applications of calculus in calculating lengths and surfaces of revolution, emphasizing integral calculus and geometric interpretations.

Introduction to DEMR

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

Euclidean Geometry: Operations and Constructions

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

Geometry II: Modern Geometric Transformations

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

Calculating Volumes of Solids: Integration Techniques

Covers the calculation of volumes of solids using integration techniques and examples of solids of revolution.

Geometric Projections: Historical Perspectives and Applications

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

Duplication of the Cube

Delves into the historical challenge of duplicating the cube, exploring construction methods, misattributions, and geometric concepts.