Lectures related to Elementary Operations in Geometry

Angle at the Center & Power of a Point

Explores angles at the center of a circle and the power of a point relative to a circle, emphasizing their importance in geometry and CAD software.

Elementary Operations in Geometry

Explores exterior angles in triangles, inscribed angles in circles, and a point's power relative to a circle.

Vectors: Definitions and Operations

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

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.

Relative Positions in Space

Covers the precise description of the relative positioning of objects in space.

Trigonometric Functions

Covers the concept of trigonometric functions and their applications in geometry.

Geometry: Euclidean Elements & Vitruvius

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

Homotheties and Translations

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

Elliptical Arch Construction

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

Geometry of Hyperbolas and Ellipses

Explores the construction of hyperbolas and ellipses, along with geometry properties and exercises on circles.

Geometry: Ellipse and Hyperbola

Explores the properties of ellipses, hyperbolas, circles, and products in geometry.

Elementary Operations in Geometry

Explores elementary operations in geometry, including addition, subtraction, multiplication, and division of segments and angles.

Mediatrix and Bisector

Explores the mediatrix and bisector properties in right-angled triangles through proofs and constructions.

Euclidean Geometry: Operations and Constructions

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

Curvature and Osculating Circle

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Projective Geometry: Fundamentals and Applications

Explores the fundamentals of projective geometry and its practical applications in solving geometric problems.

Quadrature & Trisection: Geometric Constructions

Explores non-constructible figures, emphasizing quadrature and trisection of angles, and their application in architecture.

Conformity and Compliancy in Geometry

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

Geometry and Complex Numbers: Circles in the Complex Plane

Explores equations and properties of circles in the complex plane.

Geometric Operations: Inversion & Orthogonal Circles

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