Theory & Mathematics

Core vocabulary, design thinking, geometry, and mathematical principles underlying architectural form.

91 Terms

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Angle

The figure formed by two lines meeting at a point. Angles (measured in degrees) are fundamental to geometry and form com…

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Anteroom

A small room or space leading to or serving as an entrance to a larger or more important room.

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Aperture

An opening or gap in a surface, particularly in a facade or wall. Apertures control light, ventilation, and views. They …

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Arc

A curved line that is part of a circle. Arcs are fundamental to arches, domes, and curved forms.

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Articulation

The clear expression and separation of distinct architectural elements, creating visual clarity and emphasizing structur…

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Asymmetry

The arrangement of forms without mirror symmetry, creating dynamic visual interest through balanced imbalance. Asymmetry…

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Atap Limas

A hip roof — a pitched roof with four sloping planes meeting at a ridge, with no exposed gable ends. Atap limas is widel…

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Atap Pelana

A gable or saddle roof — the simplest pitched roof form, with two sloping planes meeting at a central ridge and open tri…

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Axis

An imaginary line used to organise space, movement, or visual direction in a design. Buildings and rooms are often arran…

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Balance

The visual equilibrium of a composition, achieved through symmetry, asymmetry, or weight distribution. Balance can be fo…

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Bay

A subdivision of a building's interior or exterior, typically defined by a recurring structural or spatial module. Bays …

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Bay Window

A window that projects outward from the plane of the wall, creating extra interior space and allowing more light and vie…

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Bukaan

An opening — any aperture in a wall, floor, or roof that allows light, air, or movement to pass through. In Indonesian a…

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Chamber

A large or formal room or hall, often in governmental, institutional, or religious buildings.

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Circle

A round two-dimensional shape with all points equidistant from a center. Circles are fundamental to planning and circula…

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Circulation

The network of pathways — corridors, stairs, ramps — that allows people to move through a building. Circulation is both …

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Circumference

The perimeter or outer boundary of a form, especially a circular or curved one. In architecture, circumference refers to…

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Composition

The arrangement and organization of elements in space according to a coherent system or principle. Composition considers…

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Cone

A three-dimensional shape with a circular base tapering to a point. Cone geometry appears in structures, roofs, and scul…

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Connection

The joint between two structural members where loads are transferred. Connections are critical to structural integrity a…

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Context

The surrounding environment — physical, cultural, historical, social — that influences and constrains architectural desi…

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Contrast

The juxtaposition of opposing qualities (light-dark, rough-smooth, large-small) creating visual interest and emphasis. C…

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Core

The central zone of a building containing services — stairs, elevators, mechanical systems, bathrooms — that serve the s…

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Cornice

A horizontal ornamental molding that projects from a wall or roof edge. Cornices frame transitions between major archite…

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Corridor

A long passageway connecting rooms or spaces. Corridors are circulation elements that can be functional (narrow, minimal…

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Curve

A continuous bending line or surface without sharp angles. Curves in architecture can be structural (arches, vaults), sp…

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Cylinder

A three-dimensional shape with two parallel circular bases connected by a curved surface. Cylinders appear as columns, t…

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Datum

A reference element — a line, plane, or volume — that anchors or organises other elements in a composition. Other forms …

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Datum Line

A reference line used in design and technical drawings to establish the base elevation or alignment from which other mea…

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Diagonal

A line connecting non-adjacent corners of a polygon. Diagonals create visual dynamism and are structural in bracing syst…

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Doorway

The opening through which people pass between spaces, typically framed by a door frame. Doorways are thresholds that mar…

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Double-Height

A space that spans two floors vertically, creating a tall, dramatic interior void. Double-height spaces increase visual …

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Ellipse

A curved shape resembling a flattened circle, defined by two focal points. Ellipses create elongated, dynamic forms.

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Enclosure

The act of bounding space with walls, screens, or other elements to create a defined interior environment. Enclosure is …

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Facade

The primary exterior face of a building, usually the front-facing elevation that addresses a street or public space. The…

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Fenestration

The arrangement, proportion, and design of windows and openings in a building's facade. Fenestration affects light, vent…

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Fenestration Pattern

The systematic arrangement and rhythm of windows on building facades. Fenestration patterns affect visual composition, i…

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Fibonacci Sequence

A mathematical sequence where each number is the sum of the previous two (1, 1, 2, 3, 5, 8, 13...). The ratio approaches…

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Figure-Field

A compositional approach where a distinct architectural figure is understood against and defined by its surrounding fiel…

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Focal Point

The point or element in a composition that draws and holds visual attention. Focal points are created through emphasis, …

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Form

The three-dimensional shape or geometry of a building or object. Form encompasses the overall massing, silhouette, and a…

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Fractal

A geometric form that exhibits self-similarity at different scales — zoom in and the pattern repeats. Fractals occur in …

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Frieze

A horizontal band of decoration or ornament on a wall, typically between the architrave and cornice in classical orders.…

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Gable

The triangular section of wall at the end of a pitched roof, between the two sloping roof planes. Gables are common in r…

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Geometry

The mathematical study of shapes, sizes, and spatial relationships. Geometry is fundamental to architecture for creating…

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Gestalt

A unified whole or configuration perceived as greater than the sum of its parts. Gestalt principles explain how people p…

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Golden Ratio

A proportion, approximately 1:1.618, considered aesthetically ideal and found throughout nature, art, and architecture. …

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Golden Section

A division of a line segment into two parts such that the ratio of the larger part to the smaller equals the ratio of th…

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Grate

A framework of bars or grilles, typically made of metal, that covers an opening to allow passage of light or air while p…

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Grid

A regular network of horizontal and vertical lines used to organise structure, space, and circulation in architecture. S…

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Grille

A framework of bars, often decorative, that covers an opening or screens a surface. Grilles can be fixed or operable and…

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Ground Floor

The floor level of a building that is at or closest to street or ground level. The ground floor typically houses public …

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Harmony

The balanced and coherent relationship between the various parts of a composition, creating unity and wholeness. Harmony…

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Hexagon

A six-sided polygon with equal sides and angles (in regular hexagons). Hexagons tessellate efficiently and appear in nat…

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Hierarchy

The principle that some elements in a design are more important than others, expressed through size, position, material,…

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Hip Roof

A roof where two or more sloping planes meet at angled edges (hips) rather than having a ridge. Hip roofs slope inward f…

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Hyperbola

A mathematical curve formed by the intersection of a cone and a plane at a specific angle. Hyperbolic forms appear in ar…

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Hyperbolic Paraboloid

A three-dimensional curved surface defined by two opposing parabolic curves. Hyperbolic paraboloids create dramatic vaul…

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Hyperboloid

A three-dimensional surface generated by rotating a hyperbola around one of its axes. Hyperboloid structures are doubly …

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Infill

The act of filling in vacant space within an existing built environment, typically by constructing new buildings in gaps…

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Inflection Point

A point on a curve where the direction of curvature changes from concave to convex or vice versa. In architecture, infle…

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Layering

The organization of architectural elements in depth, creating visual complexity and spatial richness. Layering adds soph…

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Line

A one-dimensional geometric element extending infinitely in two directions. Lines define boundaries, create direction, a…

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Mapping

The process of representing space, relationships, or data visually. In architecture, mapping includes site analysis, pro…

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Materiality

The quality and expression of materials in architecture, including surface texture, color, and aging. Materiality commun…

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Mezzanine

An intermediate floor or balcony within a story, creating intermediate spaces without spanning the full floor-to-floor h…

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Modularity

The design principle of creating buildings from standardized, repeatable units (modules) that can be combined in various…

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Module

A standardised unit of measurement used to regulate the dimensions of a building and its components. Working to a module…

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Opening

A gap or passage in a wall, facade, or other structure, for access, light, or ventilation.

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Phenomenology

Phenomenology in architecture refers to the study of how people experience and perceive spaces and environments. It emph…

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Pi (π)

The mathematical constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diam…

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Platform

An elevated horizontal surface or stage, often freestanding or semi-detached.

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Polygon

A closed shape with straight sides. Common polygons include triangles, squares, pentagons, and hexagons.

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Porosity

The degree to which a building or urban area allows visual or physical permeability and visual connection. Porous design…

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Precedent

A previous example or case used as a reference or model for current work. Studying precedents informs design decisions a…

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Procession

A planned sequence of spaces through which a person moves, each one preparing them for the next. Great architecture ofte…

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Proportion

The mathematical relationship between the dimensions of a building's parts and the whole. Proportion governs whether a s…

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Pythagorean Theorem

The mathematical principle that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares o…

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Rhythm

The repetition of elements — columns, windows, bays, or structural members — at regular or varied intervals to create vi…

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Room

An enclosed space within a building, separated by walls, used for a specific function or purpose.

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Scale

The perceived size of a building or space relative to the human body or to its surroundings. A building can be physicall…

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Section

An orthographic drawing showing what a building looks like when cut through by an imaginary vertical plane. The section …

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Sine Wave

A smooth, periodic curve oscillating between maximum and minimum values. Sine waves appear in natural phenomena and comp…

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Space

An area or volume within a building designed for human use and movement.

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Spatial Sequence

The ordered progression of spatial experiences as people move through a building or landscape. Spatial sequences create …

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Symmetry

A condition in which one half of a composition mirrors the other about a central axis. Symmetry conveys stability, forma…

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Tessellation

The covering of a plane with a repeating pattern of one or more shapes, with no gaps or overlaps. In architecture, tesse…

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Threshold

A transitional space or moment marking the boundary between two different zones or conditions. Thresholds create psychol…

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Trigonometry

The branch of mathematics dealing with the relationships between angles and sides of triangles. In architecture, trigono…

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Tritisan

A wide roof overhang or eave extension that projects beyond the building wall to shade the facade from direct solar radi…

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Void

Empty or negative space in architecture, equally important to solid forms. Voids shape experience, provide light, and cr…

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