morf2 | orden y geometría

Introduction to Order and Geometry

Overview of the Class

• Architect María Inés Mónica introduces the topic of order and geometry, marking it as part 1 of a 3-part series.

• The concepts of order and organization were previously discussed in classes on spatial relationships, emphasizing their fundamental role in organizing forms and spaces.

Geometric Concepts

• The course will cover Euclidean geometry, formal operations between volumes, geometric variables such as profile, structure, metrics, proportion, symmetry, and rhythm.

• Euclidean geometry serves as a basic tool for defining architectural form while complementary tools help establish internal structure.

Understanding Order in Architecture

Defining Order

• The class aims to conceptually explore what order means in architecture by referencing Campos Baeza's quote about establishing spatial order.

• Order can manifest at various complexity levels: from cities to buildings to individual rooms.

Systematization vs. Structuring

• Systematizing involves ordering or organizing elements within a system; structuring establishes governing laws that maintain this order.

• External forms reflect internal morphological structures; these relationships include both formal and functional aspects.

Principles of Rhythm and Hierarchy

Fragmentation and Use

• Architectural volumes are fragmented based on different uses throughout the day, creating new volumetric decompositions that generate rhythms and sequences.

• Key concepts like rhythm and hierarchy are highlighted as resources used by architects to create visual interest within designs.

Visual Principles

• Basic geometric principles such as lines defined by two points allow for symmetrical arrangements; symmetry is linked with axes for distribution.

• Hierarchy gives significance to certain forms or spaces based on dimensions or relative positions.

Exploring Geometry's Role

Definition of Geometry

• Geometry is defined as a branch of mathematics focused on shape, measurement, position of elements in space, and their interrelations through specific procedures like theorems.

Importance for Architects

• Incorporating geometry is crucial for developing spatial thinking necessary for interpreting physical environments effectively.

Instrumental Use of Geometry

Understanding Geometrical Foundations in Architecture

The Role of Geometry in Architectural Education

• The importance of geometry is emphasized as a foundational element in early architectural studies, particularly through various types of geometries used in communication and representation systems.

• In Morphology 2, the focus will be on Euclidean geometry, which adheres to Euclid's five postulates and has zero curvature, contrasting with non-Euclidean geometries studied later.

Characteristics of Euclidean vs. Non-Euclidean Geometry

• A triangle's internal angles sum to 180 degrees in Euclidean geometry; however, this differs in non-Euclidean geometries like elliptic (positive curvature) and hyperbolic (negative curvature).

• In spherical geometry (convex), the sum of angles exceeds 180 degrees, while in hyperbolic geometry (concave), it is less than 180 degrees.

Exploring Euclid's Five Postulates

• The course will delve into the five fundamental postulates established by Euclid that define plane geometry:

• Two distinct points determine a line segment.

• A line segment can be extended indefinitely.

• A circle can be drawn with any center and radius.

• All right angles are equal.

• Through a point outside a line, only one parallel can be drawn.

Implications for Parallel Lines

• In flat geometry, parallel lines remain equidistant; however:

• In spherical geometry, they converge due to convexity.

• In hyperbolic geometry, they diverge because of concavity.

Application of Geometric Concepts in Architecture

• Understanding these geometric principles helps explain external forms in architecture as products of their internal geometric structures.

• Despite advancements since Euclid’s time over two millennia ago, his concepts remain relevant for understanding spatial configurations even though reality may not conform strictly to linear or planar models.

Basic Elements Defined by Euclid

• Key geometric elements include:

• Point: Intersection of segments; static and non-directional.

• Line: Directional boundary indicating contours or intersections between planes.

• Plane: Enveloping surface defining volumes; can be solid or hollow.

Transformations within Three-Dimensional Space

• The exploration includes how volumes relate to space through transformations such as:

• Translation: Movement without altering shape or size.

• Rotation: Change in direction around an axis based on coordinates.

• Reflection: Symmetrical flipping across a plane.

• Homothety: Resizing without changing shape but altering position.

Geometric Concepts and Architectural Applications

Overview of Geometric Bodies

• The discussion begins with a recap of geometric bodies, highlighting the classification of regular polyhedra (Platonic solids) and irregular polyhedra, as well as round bodies.

• The focus will be on exploring new forms using only cubes and prisms, avoiding other Platonic solids and round bodies for formal generation exercises.

Formal Generation in Geometry

• Emphasis is placed on generating new shapes through basic volumes while applying Euclidean geometry operations and geometric variables.

Architectural Examples

• Architectural examples illustrate the use of order in design, showcasing how primary elements structure space. A U-shaped house layout is discussed.

• The façade features a straight line defining the volume profile, emphasizing size hierarchy among different sections of the house.

Design Intentions

• Another example presents a main space with secondary areas, creating a unified façade characterized by alternating solid and void patterns.

• The concept of lines is explored further; they are perceived not just as dimensions but also as structural support elements in architecture.

Spatial Relationships

• Observations on an elevated base plane reveal how mass characterizes volumes while maintaining rhythm through solid and void relationships that correspond to living spaces.

• A specific house design near Mar Azul illustrates social versus private spaces at level 0, integrating mid-level connectors within its volumetric prism structure.

Materiality and Conceptual Design

• Concrete planes serve both as enveloping structures and functional elements throughout the façade, reinforcing the idea of planes dominating architectural details.

• Interior spaces reflect this plane concept through vertical divisions that define living areas without rigid boundaries.

Advanced Spatial Conception

• An architect's sketch demonstrates broken horizontal planes intersecting with vertical ones, illustrating advanced spatial concepts like "decomposing the box."

• This approach leads to intermediate spaces that blur interior-exterior boundaries, promoting fluidity in spatial experience.

Further Reading Suggestions