Flat Geometric Shapes in Architecture

Course Content Overview

• The course, "Flat Geometric Shapes, Properties & Interpretation," is a first-year project theory course at the University of Algiers 1, Faculty of Sciences, Department of Architecture.
• The course duration is 2023-2024.
• The course instructor is Dr. DJEDOUANI Racha.

Introduction to Geometric Shapes in Architecture

• Geometric shapes in architecture are more than just aesthetics; they also have functional, structural, and symbolic implications.
• Architects use geometric shapes to create spaces that are visually appealing, functional, and architecturally meaningful.

Definition of Geometric Shape

• A geometric shape is defined by boundaries, lines, or edges with specific mathematical properties.
• These shapes have characteristics like length, width, height, angles, and proportions.

Basic Concepts of Geometry

• Fundamental concepts like points, lines, angles, polygons, and circles are crucial for understanding geometric shapes used in architecture.

1. Points

• Points are the basic building blocks in geometry.
• In architecture, points represent precise locations in space (often described using coordinates x, y, z).
• Points serve as reference markers for defining other geometric elements, and are the foundation for layout and measurement.

2. Lines

• Lines (connected series of points) are one-dimensional geometric elements.
• Architects use lines to create frameworks for structures, define edges (walls, roofs), and influence the overall style and form of a building.
• Lines can be straight, curved, horizontal, vertical, oblique, and their intersections create angles.

3. Angles

• Angles are formed by the intersection of two lines.
• Understanding angles is vital in architecture for determining orientation, alignment of elements, and visual effects.
• Different angles (acute, right, obtuse, reflex, straight) create distinct visual effects and impact how a building interacts with light and space.

4. Polygons

• Polygons are two-dimensional shapes formed by connecting straight lines (three or more sides).
• Polygons are extensively used in architecture to design floor plans, facades, and layouts, influencing both aesthetics and functionality.
• Specific polygons (triangles, squares, rectangles, pentagons, hexagons, heptagons, octagons, and decagons) have particular properties, like the sum of interior angles.

5. Circles

• A circle is a closed curve where all points are equidistant from the center.
• Circles are defined by their radius (distance from the center to edge) and diameter (twice the radius).
• Architects use circles to create curved or circular elements, such as arches, domes, and circular windows.

Properties of Geometric Shapes

• Architects employ geometric shape properties like symmetry, asymmetry, proportion, and balance to create aesthetically pleasing, functional, and harmonious buildings.

1. Symmetry

• Identical halves of a shape, mirrored across a central axis or plane.
• Symmetry helps create balanced and formal appearances, common in classical buildings (palaces, government buildings).

2. Asymmetry

• The opposite of symmetry; the shape does not have mirrored halves.
• Used to create visual interest and dynamism, typical of contemporary architecture.

3. Proportion

• The relationship between different parts of a building or an architectural element in relation to the whole. Architectural principles use calculated ratios to create balanced and aesthetically pleasing structures.

4. Balance

• The distribution of architectural elements in space to avoid visual imbalance.
• Both symmetrical and asymmetrical arrangements ensure functionality and safety of the building.

Influence on Architectural Design

• Aesthetics: Shapes contribute to pleasing and classical aesthetics (symmetry, proportion), or contemporary character (asymmetry).
• Functionality: Well-proportioned or balanced shapes optimize functionality, ensuring stability in the face of wind and earthquakes.
• Comfort: Spatial proportions affect comfort. Well-designed interior proportions improve usability.
• Expression: Symmetry or asymmetry, and proportion are used to express architectural ideas visually (dynamic vs. stable).

Additional Architectural Concepts

• Geometric Terminology:
  • Plane: A flat surface extending infinitely.
  • Elevation: An orthogonal view of a building façade or side, showing structure viewed externally.
  • Section: An orthogonal view, revealing interior layout (an imaginary cut).
  • Coordinates: Numerical values to specify points in space.
  • Axis: An imaginary line used for rotation reference and defining symmetry.
  • Regular Polygon: Polygons with equal sides and angles; used in designs.
  • Tessellation: Repetition of a geometric pattern to entirely cover a surface.
• Architectural Examples: Specific examples of architecture are featured to illustrate application of geometric concepts (Heydar Aliyev Cultural Centre, Fallingwater, Villa Savoye, Sydney Opera House).
• Scale and Projection:
  • Scale: Reducing object sizes for practical representations (architectural plans).
  • Projection: How an image is displayed on a surface.
• Symbolism:
  • Geometric shapes can represent cultural meanings in certain cultures (Circle = unity).
• Innovation:
  • Architects use complex geometric shapes for unique and innovative building designs.
• Integration with Environment:
  • Geometric shapes can be used to blend a building naturally into its surroundings (i.e. a pyramid-shaped building on a mountain).

Conclusion

• Understanding geometric principles is foundational to architect's skill, allowing them to create both functional and aesthetically pleasing structures.