Lectures related to Homotheties and Translations

Explores translations and homotheties, discussing their properties and practical applications in preserving geometric characteristics.

Covers translations, homotheties, and their geometric properties, including reversibility and composition.

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

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

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

Explores reflection and rotation composition in analytical geometry, including finding centers and solving fixed point systems.

Covers translations, homotheties, and their analytical expressions, emphasizing stability by composition.

Explores rotation in analytical geometry, including center coordinates and fixed points.

Explores geometric transformations like translation and homothety in the plane.

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

Covers Cartesian equations in analytical geometry, focusing on encoding line directions and unique equations.

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

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

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

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

Explores linear similarities and similitudes, demonstrating their properties and applications in geometry.

Explores the synthesis of plane isometries and their composition through axial reflections, rotations, translations, and glided reflections.

Explores normal equations of lines in the plane through point translation for precision.

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

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.