C01 Flat Geometrical Shapes, Properties & Interpretation PDF

# C01: Flat Geometrics Shapes, Properties & Interpretation ## People's Democratic Republic of Algeria - Ministry of Higher Education and Scientific Research - Univeristy of Algiers 1 - Faculty of Sciences - Department of Architecture - 1st year project theory course ## 2023-2024 ## Dr. DJEDOUANI...

# C01: Flat Geometrics Shapes, Properties & Interpretation ## People's Democratic Republic of Algeria - Ministry of Higher Education and Scientific Research - Univeristy of Algiers 1 - Faculty of Sciences - Department of Architecture - 1st year project theory course ## 2023-2024 ## Dr. DJEDOUANI Racha - [email protected] - www.researchgate.net/profile/Racha-Djedouani ## Course Content - Introduction - Definition of geometric Shape - Basic concepts of geometry - Properties of geometric shapes - Influence on Architectural Design - Role of the geometric shapes on Architectural Design - Historical examples of the use of geometric shapes in architecture - Geometric Terminology for Architects - Conclusion ## Introduction - Geometric shapes in architecture are not merely aesthetic elements but also have functional, structural, and symbolic implications. - Architects employ geometric shapes to craft spaces that are visually appealing, functional, and architecturally meaningful ## Definition of Geometric Shape - A geometric shape is a shape defined by boundaries, lines, or edges with specific mathematical properties. - These shapes often have characteristics such as length, width, height, angles, and proportions. - ## Basic Concepts of Geometry - Points, lines, angles, polygons, circles - These concepts, such as points, lines, angles, and polygons, circles, form the basis for understanding geometric shapes in architecture. ## 1. Points - Points are the most basic elements in geometry. In architecture, a point represents a precice location in space, often identified using coordinates (x, y, z) in three-dimensional space. - Points are used as reference markers for defining other geometric elements such as lines, shapes, and structures. - They are the starting point for any architectural design, serving as the basis for layout and measurement. ## 2. Lines - Lines (a series of connected points) are one-dimensional geometric objects that connect two points. - In architectural design, lines play a role in creating the framework for structures. - Architects use lines to define the edges of walls, roofs, and other architectural elements. - The arrangement of lines influences the overall form and style of a building. - Lines can be straight or curved, horizontal or vertical or oblique, and their intersection gives rise to angles. ### Types Of Lines - **Horizontal Line:** The lines drawn horizontally are called horizontal lines. - **Vertical Line:** The lines drawn vertically are called vertical lines. - **Slanting Line:** The lines drawn in a slanting position are called oblique or slanting lines. - **Parallel Lines:** - **Straight Line:** - **Intersecting Lines:** - **Curved Line:** - **Perpendicular Lines:** ## 3. Angles - Angles are formed when two lines intersect at a common point. - Understanding angles is important in architecture because they determine the orientation and alignment of structural elements. - Different angles can create diverse visual effects and impact how a building interacts with light and space. ### Types of Angles - **Acute Angle:** - **Right Angle:** - **Obtuse Angle:** - **Reflex Angle:** - **Straight Angle:** ## 4. Polygons - Polygons are two-dimensional shapes formed by connecting multiple straight-line segments. They can have three or more sides. - In architecture, polygons are used extensively to design floor plans, facades, and layouts. The choice of polygonal shapes influences the aesthetics and functionality of a building. ### Types of Polygons - **Triangle:** 180 degrees - **Square:** 360 degrees - **Rectangle:** 360 degrees - **Pentagon:** 540 degrees - **Hexagon:** 720 degrees - **Heptagon:** 900 degrees - **Octagon:** 1080 degrees - **Decagon:** 1440 degrees ### Polygons Types - **Triangle:** A polygon with three sides. Different types of trangles include: - **Equilateral:** 3 equal sides, all angles 60 degrees. - **Isosceles:** 2 equal sides, 2 equal angles. - **Scalene:** No equal sides, no equal angles. - **By Angle:** - **Right:** 1 angle = 90° - **Acute:** All angle < 90° - **Obtuse:** 1 angle > 90° #### Polygons Types: - **Triangle:** - Has 3 sides and 3 vertices - Has no diagonals - Sum of the interior angles is 180° - **Pentagon:** - Has 5 sides and 5 vertices - Has 5 diagonals - Sum of the interior angles is 540° - **Heptagon:** - Has 7 sides and 7 vertices - Has 14 diagonals - Sum of the interior angles is 900° - **Nonagon:** - Has 9 sides and 9 vertices - Has 27 diagonals - Sum of the interior angles is 1260° - **Quadrilateral:** - Has 4 sides and 4 vertices - Has two diagonals - Sum of the interior angles is 360° - **Hexagon:** - Has 6 sides and 6 vertices - Has 9 diagonals - Sum of the interior angles is 720° - **Octagon:** - Has 8 sides and 8 vertices - Has 20 diagonals - Sum of the interior angles is 1080° - **Decagon:** - Has 10 sides and 10 vertices - Has 35 diagonals - Sum of the interior angles is 1440° ## 5. Circle - A circle is a special geometric shape that is not a polygon. It is a closed curve characterizded by all points on its circumference being equidistant from its center. - The circle is defined by its radius (the distance from the center to the edge) and its diameter (twice the radius). - Circles are commonly used in architecture to create curved or circular architectural elements such as arches, domes, and circular windows. ## Properties of Geometric Shapes (Symmetry, asymmetry, proportion, balance) - Architects use these properties to create buildings that are aesthetically pleasing, functional, and harmonious. ## 1. Symmetry - Symmetry is a property of geometric shapes in which one half is a mirror image of the other half with respect to a central axis or a plane of symmetry. - Symmetry can be used to create a balanced and harmonious aesthetic in architectural design. - Symmetrical buildings often have a classical and formal appearance, such as palaces and government buildings. ## 2. Asymmetry - Asymmetry is the opposite of symmetry, where architectural elements are not replicated exactly on either side of a central axis. - Asymmetry can create visulal interest and dynamism in design. It is often used in contemporary architecture to convey a sense of modernity and uniqueness. ## 3. Proportion - Proportion relates to the relationship between different parts of a building or architectural element in relation to the whole. - Architects use carefully calculated proportion ratios to create buildings the appear balanced and aesthetically pleasing. - For example, the ratio between the height of a column and the width of its base may be determined by classical proportion principles. ## 4. Balance - Balance is a fundamental concept in architectural design. It involves ensuring that architectural elements are distributed in space in a balanced way to avoid visual imbalance. - Balance can be either symmetrical or asymmetrical, but the goal is to create a sense of visual stability. Balance is essential for the functionality and safety of a building ## Influence on Architectural Design ### Aesthetics - Symmetry and proportion can contribute to a pleasing and classical aesthetic, while asymmetry can bring originality and a contemporary character. ### Functionality - Balance is essential for the structural stability of a building, ensuring it withstands external forces such as wind and earthquakes. ### Comfort - Proportion can influence the ergonomics and comfort of interior spaces. For example, well-proportioned ceiling heights can make a space more inviting. ### Expression - Architecture often uses symmetry, asymmetry, proportion, and balance to express ideas and conceptual intentions. - For example, an asymmetrical building may express dynamism and change, while a symmetrical or may evoke stability and tradition. ## Role of Geometric Shapes in Architectural Design - **1. Aesthetics and harmony:** Carefully designed geometric shapes can create visual beauty and harmony within a building or space. They contribute to crafting balanced compositions that are visually pleasing. - **2. Functionality:** Geometric shapes can be used to optimize the functionality of spaces. For example, rectangular shapes can be effective in delineating work areas in an office, while circular shapes can facilitate movement in a meeting room. - **3. Structure and stability:** Geometric shapes are essential for the structural stability of buildings. Triangles and arches, for instance, are commonly used geometric shapes to support loads and ensure durability. - **4. Symbolism:** Some geometric shapes hold symbolic meanings in different cultures. For example, a circle may represent unity or perfection, while a square may evoke stability and security. Architects can play with these symbols to convey messages and meanings. - **5. Innovation:** Contemporary architects often use complex and unconventional geometric shapes to create unique and innovative buildings. These shapes can challenge conventions and push the boundaries of architectural creativity. - **6. Integration into the environment:** Geometric shapes can be used to integrate a building into its natural or urban surroundings. For example, a pyramid-shaped building may harmonize with mountainous topography, while a cube-shaped building can blend into a modern urban environment. ## Geometric Terminology for Architects ### Plane - In geometry, a plane is a flat surface that extends infinitely in all directions. Planes are used to represent the horizontal or vertical surfaces of buildings, such as floors, ceilings, and walls. ### Elevation - An elevation is an orthogonal view of a building's facade or side. It shows how the building appears when viewed from the outside, typically in a vertical projection. ### Section - A section is an orthogonal view of a building or a portion of it, showing what would happen if the building were cut horizontally or vertically. Section are used to reveal the interior of a building and its layout. ### Coordinates - Coordinates are numerical values that define the position of a point in a reference system. In architecture, coordinates are often used to specify the location of points in a plan or three-dimensional space. ### Axis - An axis is an imaginary line used as a reference around which a geometric shape can rotate. Axes are often used to describe symmetry and alignment in architectural design. ### Center - The center of a geometric shape, such as a circle or square, is the point equidistant from all points on its circumference or sides. The center is often a key point in creating balanced compositions. ### Regular polygon - A regular polygon is a geometric shape with all its sides of the same length and all its angles of the same measure. Regular polygons are often used in the design of architectural plans. ### Tessellation - Tessellation is the repetition of a geometric pattern to cover a flat surface without leaving empty spaces or overlaps. It can be used to create decorative patterns in architecture. ### Scale - Scale refers to the relative size of an object compared to its actual size. Architectural plans are often drawn to a reduced scale for practical reasons. ### Projection - Projection is how an image or shape is projected onto a flat surface. Architects use different types of projection to represent three-dimensional objects on plans. ## Conclusion - In conclusion, understanding and mastering the properties of geometric shapes are important for architects, as they enable them to create buildings that are not only functional but also aesthetically pleasing and expressive.