IN BRIEF Central symmetry: transformation around a point, preserving the properties of the original figure. Construction of symmetricals: procedure to obtain the symmetrical of a point, a segment, or a figure. Center of symmetry: a point O if its symmetrical is identical to the figure. Geometric transformation: symmetry is an involutive form, preserving parallelism. Applications: … Read more
IN BRIEF Geometric transformations: Mechanisms for modifying figures 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. Various applications: Used in various fields such as physics and computer science. Pedagogical approach: Presentation and exercises in student textbooks. … Read more
IN BRIEF Geometry as the foundation of modern architecture Use of basic geometric shapes for strength 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 a Cartesian coordinate system. Use of vectors to determine equations of lines. Study of intersections between lines and circles. Properties of circles: … Read more
IN SHORT Symmetry: A fundamental concept in physics, reflecting the invariance of a system in the face of transformations. Transformations: Symmetries can be associated with modifications 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 … Read more