Geometry

1. Applications of Geometry
   1. Art and Design
      1. Symmetry and Patterns
         1. Types of symmetry (bilateral, radial)
         2. Use of symmetry in artworks
         3. Tessellations and tilings
         4. Geometric patterns in textiles and surface decoration
      2. Perspective and Proportion
         1. One-point, two-point, and three-point perspective
         2. Golden ratio in art
         3. Proportional relationships in figure drawing
         4. Influence of geometry on graphic design
   2. Architecture
      1. Structural Analysis and Design Principles
         1. Load distribution and stress analysis
         2. Geometric principles in bridge and arch designs
         3. Use of triangles and other polygons in structures
      2. Use of Geometric Forms
         1. Domes, arches, and vaults
         2. Geodesic structures
         3. Modular design using geometric shapes
         4. Influence of geometry in classical and modern architecture
   3. Engineering
      1. Computer-Aided Design (CAD) and Mechanical Design
         1. Role of geometry in modeling and simulations
         2. Geometric constraints in CAD software
         3. Precision and scalability in engineering design
      2. Stress and Load Analysis
         1. Finite element analysis (FEA) using geometric meshes
         2. Geometric representations of complex shapes in mechanics
         3. Optimization of mechanical components using geometric modeling
   4. Physics
      1. Geometric Optics
         1. Light reflection and refraction using geometric models
         2. Lenses and mirrors: focal length, converging/diverging rays
         3. Wavefronts and ray diagrams
      2. Study of Spacetime Geometry in Relativity
         1. Einstein's theories and geometric interpretations
         2. Curvature of spacetime and its effects on light and objects
         3. Geodesics as paths of least action or shortest distance
   5. Other Applications
      1. Geography and Cartography
         1. Use of geometry in map projections and spatial analysis
         2. Triangulation and measurement of land
      2. Computer Science
         1. Computational geometry algorithms
         2. Image processing and graphics using geometric transformations
      3. Medicine and Biology
         1. Radiography and CT scanning: geometric reconstructions
         2. Geometric modeling in biomechanics and prosthetics