IN BRIEF Central symmetry: transformation around a point, preserving the properties of the original figure. Construction of symmetric figures: procedure to obtain the symmetric of a point, segment, or figure. Center of symmetry: a point O if its symmetric is identical to the figure. Geometric transformation: symmetry is an involutive form, preserving parallelism. Applications: symmetry … Read more
IN BRIEF Geometric transformations : Mechanisms for modifying shapes in the plane. Main types : Translation, Rotation, Reflection, Dilation. Bijectivity : Unique association between original points and image points. Conservations : Lengths, angles, areas, and alignments preserved during transformations. Varied applications : Used in various fields such as physics and computer science. Pedagogical approach : … Read more
IN BRIEF Geometry as the foundation of modern architecture Use of basic geometric shapes for solidity and aesthetics Importance of proportions and symmetries in design Role of mathematics in predictive models Application of sacred geometry for harmonious proportions New modeling tools for contemporary architecture Relationships between nature and architecture through geometry Modern architecture relies on … Read more
IN BRIEF Analytical Geometry: study of geometric figures using equations. Reduced equation of a line: y = mx + p, where m is the slope. Analysis of the line and the circle in an orthonormal coordinate system. Use of vectors to determine line equations. Study of the intersections between lines and circles. Properties of circles: … Read more
IN BRIEF Symmetry: A fundamental concept in physics, reflecting the invariance of a system under transformations. Transformations: Symmetries can be associated with changes such as rotations or inversions. Symmetry groups: A mathematical structure that formalizes the relationships between symmetries and physical laws. Conservation: Each symmetry leads to the conservation of a physical quantity, according to … Read more