IN BRIEF Central symmetry: transformation around a point, conserving the properties of the original figure. Construction of symmetrics: procedure to obtain the symmetric of a point, segment, or figure. Centre of symmetry: a point O if its symmetric is identical to the figure. Geometric transformation: symmetry is an involutive form, preserving parallelism. Applications: symmetry is … Read more
IN BRIEF Geometric transformations: Mechanisms for modifying figures in the plane. Main types: Translation, Rotation, Reflection, Homothety. 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: 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 Relations between nature and architecture through geometry Modern architecture relies on … Read more
IN BRIEF Analytic geometry: study of geometric figures using equations. Slope-intercept form 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 intersections between lines and circles. Properties of circles: equations … Read more
IN BRIEF Symmetry: 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: Mathematical structure that formalizes the relationships between symmetries and physical laws. Conservation: Each symmetry leads to the conservation of a physical quantity, according to Noether’s theorem. … Read more