ARCHITECTURE Form, Space, & Order Fourth Edition ARCHITECTURE Form, Space, ISBN (paperback); (ebk);. Includes bibliographical references and index. ISBN (pbk.) 1. Architecture--Composition, proportion, etc. 2. Space (Architecture) I. Title. Architecture--form, space, & order / Francis D.K. Ching. -- 3rd ed. p. cm. Includes bibliographical references and index. ISBN (pbk.) 1.
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Four Planes: Closure Four vertical planes establish the boundaries of an introverted space and influence the field of space around the enclosure. Standing upright and alone, a slender linear element is nondirectional except for the path that would lead us to its position in space. Any number of horizontal axes can be made to pass through it. When located within a defined volume of space, a column will generate a spatial field about itself and interact with the spatial enclosure. A column attached to a wall buttresses the plane and articulates its surface.
At the corner of a space, a column punctuates the meeting of two wall planes. Standing free within a space, a column defines zones of space within the enclosure.
When centered in a space, a column will assert itself as the center of the field and define equivalent zones of space between itself and the surrounding wall planes.
When offset, the column will define hierarchical zones of space differentiated by size, form, and location. Linear elements serve this purpose in marking the limits of spaces that require visual and spatial continuity with their surroundings. Two columns establish a transparent spatial membrane by the visual tension between their shafts. Three or more columns can be arranged to define the corners of a volume of space.
This space does not require a larger spatial context for its definition, but relates freely to it. The edges of the volume of space can be visually reinforced by articulating its base plane and establishing its upper limits with beams spanning between the columns or with an overhead plane. A repetitive series of column elements along its perimeter would further strengthen the definition of the volume.
In the example above, the tokobashira, often a tree trunk in natural form, is a symbolic element that marks one edge of the tokonoma in a Japanese tearoom. Piazza of St. Four columns can establish the corners of a discrete volume of space During the Renaissance, Andrea Palladio incorporated the tetrastyle theme in within a larger room or setting.
Supporting a canopy, the columns form the vestibules and halls of a number of villas and palazzi. The four columns not an aedicule, a diminutive pavilion that serves as a shrine or the symbolic only supported the vaulted ceiling and the floor above but also adjusted the center of a space.
Traditional Roman houses typically were organized about an atrium open In the Sea Ranch condominium units, four posts along with a sunken floor and to the sky and surrounded by a roof structure supported at the corners by an overhead plane define an intimate aedicular space within a larger room. Vitruvius termed this a tetrastyle atrium. Condominium Unit No.
Michel, France, — A regularly spaced series of columns or similar vertical elements form a colonnade. This archetypal element in the vocabulary of architectural design effectively defines an edge of a spatial volume while permitting visual and spatial continuity to exist between the space and its surroundings. A row of columns can also engage a wall and become a pilastrade that supports the wall, articulates its surface, and tempers the scale, rhythm, and proportioning of its bays.
A grid of columns within a large room or hall not only serves to support the floor or roof plane above.
The orderly rows of columns also punctuate the spatial volume, mark off modular zones within the spatial field, and establish a measurable rhythm and scale that make the spatial dimensions comprehensible.
This type of construction, in particular the use of concrete columns to support floor and roof slabs, afforded new possibilities for the definition and enclosure of spaces within a building. Interior spaces could be defined with non-load-bearing partitions, and their layout could respond freely to programmatic requirements. Sketches for The Five Points of the New Architecture, , Le Corbusier On the facing page, two contrasting examples of the use of a column grid are illustrated: A column grid establishes a fixed, neutral field of space in which interior spaces are freely formed and distributed.
A grid of columns or posts corresponds closely to the layout of the interior spaces; there is a close fit between structure and space. A round column has no preferred direction except for its vertical axis. A square column has two equivalent sets of faces and therefore two identical axes. A rectangular column also has two axes, but they differ in their effect. As the rectangular column becomes more like a wall, it can appear to be merely a fragment of an infinitely larger or longer plane, slicing through and dividing a volume of space.
A vertical plane has frontal qualities. Its two surfaces or faces front on and establish the edges of two separate and distinct spatial fields. These two faces of a plane can be equivalent and front similar spaces.
Or they can be differentiated in form, color, or texture, in order to respond to or articulate different spatial conditions.
A vertical plane can therefore have either two fronts or a front and a back. The field of space on which a single vertical plane fronts is not well-defined. The plane by itself can establish only a single edge of the field.
To define a three- dimensional volume of space, the plane must interact with other elements of form. When 2-feet high, a plane defines the edge of a spatial field but provides little or no sense of enclosure. When waist-high, it begins to provide a sense of enclosure while allowing for visual continuity with the adjoining space.
When it approaches our eye level in height, it begins to separate one space from another.
Above our height, a plane interrupts the visual and spatial continuity between two fields and provides a strong sense of enclosure. The surface color, texture, and pattern of a plane affect our perception of its visual weight, scale, and proportion.
When related to a defined volume of space, a vertical plane can be the primary face of the space and give it a specific orientation. It can front the space and define a plane of entry into it. It can be a freestanding element within a space and divide the volume into two separate but related areas. Agostino, Rome, —, Giacomo da Pietrasanta larger volume. The partitions never form closed, geometrically static areas. While this field is strongly defined and enclosed at the corner of the configuration, it dissipates rapidly as it moves away from the corner.
The introverted field at the interior corner becomes extroverted along its outer edges. While two edges of the field are clearly defined by the two planes of the configuration, its other edges remain ambiguous unless further articulated by additional vertical elements, manipulations of the base plane, or an overhead plane.
If a void is introduced to one side of the corner of the configuration, the definition of the field will be weakened. The two planes will be isolated from each other and one will appear to slide by and visually dominate the other. If neither plane extends to the corner, the field will become more dynamic and organize itself along the diagonal of the configuration. One of the arms of the configuration can be a linear form that incorporates the corner within its boundaries while the other arm is seen as an appendage to it.
Or the corner can be articulated as an independent element that joins two linear forms together. A building can have an L-shaped configuration to establish a corner of its site, enclose a field of outdoor space to which its interior spaces relate, or shelter a portion of outdoor space from undesirable conditions around it. L-shaped configurations of planes are stable and self- supporting and can stand alone in space.
Because they are open-ended, they are flexible space-defining elements. They can be used in combination with one another or with other elements of form to define a rich variety of spaces. Typically, sheltered by the building form and to which interior spaces can be directly one wing contains the communal living spaces while the other contains related.
In the Kingo Housing estate, a fairly high density is achieved with this private, individual spaces. The service and utility spaces usually occupy a type of unit, each with its own private outdoor space. The outdoor space enclosed by the architect's studio in Helsinki is used as an amphitheater for lectures and social occasions.
It is not a passive space whose form is determined by the building that encloses it. Rather, it asserts its positive form on the shape of its enclosure. The History Faculty Building at Cambridge uses a seven-story, L-shaped block to functionally and symbolically enclose a large, roof-lit library, which is the most important space in the building.
The open ends of the field, established by the vertical edges of the planes, give the space a strong directional quality.
Its primary orientation is along the axis about which the planes are symmetrical. Since the parallel planes do not meet to form corners and fully enclose the field, the space is extroverted in nature. The definition of the spatial field along the open ends of the configuration can be visually reinforced by manipulating the base plane or adding overhead elements to the composition.
The spatial field can be expanded by extending the base plane beyond the open ends of the configuration. This expanded field can, in turn, be terminated by a vertical plane whose width and height is equal to that of the field. If one of the parallel planes is differentiated from the other by a change in form, color, or texture, a secondary axis, perpendicular to the flow of the space, will be established within the field.
Openings in one or both of the planes can also introduce secondary axes to the field and modulate the directional quality of the space. Sets of parallel vertical planes can be transformed into a wide variety of configurations. Their spatial fields can be related to one another either through the open ends of their configurations or through openings in the planes themselves. Apollinare in Classe, Ravenna, Italy, — Champ de Mars, Paris The directional quality and flow of the space defined by parallel planes are naturally manifested in spaces used for circulation and movement, such as the streets and boulevards of towns and cities.
These linear spaces can be defined by the facades of the buildings fronting them, as well as by the more permeable planes established by colonnades, arcades, or rows of trees.
The parallel planes that define a circulation space can be solid and opaque to provide privacy for the spaces along the circulation path. The planes can also be established by a row of columns so that the circulation path, open on one or both of its sides, becomes part of the spaces through which it passes.
Their repetitive pattern can be modified by varying their length or by introducing voids within the planes to accommodate the dimensional requirements of larger spaces.
These voids can also define circulation paths and establish visual relationships perpendicular to the wall planes. The slots of space defined by parallel wall planes can also be modulated by altering the spacing and configuration of the planes. They not only provide structural support for the floors and roofs of each housing unit, but also serve to isolate the units from one another, curb the passage of sound, and check Entry level the spread of fire.
The pattern of parallel bearing walls is particularly appropriate for rowhousing and townhouse schemes where each unit is provided with two orientations. At the closed end of the configuration, the field is well defined. Toward the open end of the configuration, the field becomes extroverted in nature. The open end is the primary aspect of the configuration by virtue of its uniqueness relative to the other three planes. It allows the field to have visual and spatial continuity with the adjoining space.
The extension of the spatial field into the adjoining space can be visually reinforced by continuing the base plane beyond the open end of the configuration. If the plane of the opening is further defined with columns or overhead elements, the definition of the original field will be reinforced and continuity with the adjoining space will be interrupted.
If the configuration of planes is rectangular and oblong in form, the open end can be along its narrow or wide side. In either case, the open end will remain the primary face of the spatial field, and the plane opposite the open end will be the principal element among the three planes of the configuration. If the field is entered through the open end of the configuration, the rear plane, or a form placed in front of it, will terminate our view of the space. If the field is entered through an opening in one of the planes, the view of what lies beyond the open end will draw our attention and terminate the sequence.
If the end of a long, narrow field is open, the space will encourage movement and induce a progression or sequence of events. If the field is square, or nearly square, the space will be static and have the character of a place to be in, rather than a space to move through. If the side of a long, narrow field is open, the space will be susceptible to a subdivision into a number of zones. U-shaped configurations of building forms and organizations have the inherent ability to capture and define outdoor space.
Their composition can be seen to consist essentially of linear forms. The corners of the configuration can be articulated as independent elements or can be incorporated into the body of the linear forms. They can also focus on an important or significant element within their fields. When an element is placed along the open end of its field, it gives the field a point of focus as well as a Sacred Precinct of Athena,Pergamon, Asia Minor, 4th century B.
A U-shaped building form can also serve as a container and can organize within its field a cluster of forms and spaces. The cells form an enclave for a village of community rooms. Athens early Anatolian or Aegean house U-shaped enclosures of interior space have a specific orientation toward The Hotel for Students at Otaniemi, Finland, by Alvar Aalto, demonstrates the their open ends. These U-shaped enclosures can group themselves around use of U-shaped enclosures to define the basic unit of space in double-loaded a central space to form an introverted organization.
These units are extroverted. They turn their back on the corridor and orient themselves to the exterior environment. CL O SURE Four vertical planes encompassing a field of space is probably the most typical, and certainly the strongest, type of spatial definition in architecture.
Since the field is completely enclosed, its space is naturally introverted. To achieve visual dominance within a space or become its primary face, one of the enclosing planes can be differentiated from the others by its size, form, surface articulation, or by the nature of the openings within it.
Well-defined, enclosed fields of space can be found in architecture at various scales, from a large urban square, to a courtyard or atrium space, to a single hall or room within a building complex. The examples on this and the following pages illustrate enclosed spatial fields in both urban and building-scale situations. Historically, four planes have often been used to define a visual and spatial field for a sacred or significant building that stands as an object within the enclosure.
The enclosing planes may be ramparts, walls, or fences that isolate the field and exclude surrounding elements from the precinct. The enclosure may consist of arcades or gallery spaces that promote the inclusion of surrounding buildings into their domain and activate the space they define. Plan of the Agora at Priene and its surroundings, 4th century B.
Forum at Pompeii, 2nd century B. The examples on these two pages illustrate the use of enclosed volumes of space as ordering elements about which the spaces of a building can be clustered and organized.
These organizing spaces can generally be characterized by their centrality, their clarity of definition, their regularity of form, and their dominating size. They are manifested here in the atrium spaces of houses, the arcaded cortile of an Italian palazzo, the enclosure of a Greek House No.
In contrast, other buildings can be seen to be dominated by the form of their exterior, enclosing wall planes. Exterior walls determine to a great extent the visual character of a building, whether they have the weight and opacity of load-bearing walls, the lightness and transparency of nonbearing curtain walls supported by a structural framework of columns and beams, or a combination of both.
The transition from bearing-wall constructions to frame structures have given rise to new forms that go beyond the timeless elements of basic statics—the columns, beams, and load-bearing walls of stable constructions that are fixed in time and space.
The rational forms of rectilinear geometry and the rule of the vertical have been revised, both statically and optically, by the development of irregular structures that rely on tension and friction rather than pressure. We can see these new forms as they mimic topography, orient themselves toward views, embrace sunlight, and turn away from cold winds and stormy weather. E N C L OS URE The evolution of materials and technology for separating the skin of a building from its structure has also played a major role in the development of building forms.
Structural glass facades integrate structure and cladding to provide maximum transparency in buildings. Many of the structural systems use trusses or trussed supports, which may slope inward or outward, or follow a curved geometry in plan or section.
Some use glass fines set perpendicular to the glass facade to provide lateral support. Gridshells are form-active structures that derive their strength from their double-curved surface geometry. The system uses a network of in-plane prestressed cables to provide stability and shear resistance to the thin shell grid.
Vaulted, domed, and other double- curved configurations can be used in vertical and overhead applications as well as to form complete building enclosures. The diagonal members are capable of carrying both gravity and lateral loads through triangulation, which results in a relatively uniform load distribution. This exoskeletal framework allows for the possible reduction in the number of internal supports, saving on space and building materials and providing for greater flexibility in interior layouts.
Also, because each diagonal can be viewed as providing a continuous load path to the ground, the number of possible load paths in case of a localized structural failure results in a high degree of redundancy. This project uses a structural diagrid system positioned on the outside of and very close to the glass facade to create a visually unique exterior. Similar to the growth pattern of trees, the diagrid members get thinner and more numerous with a higher ratio of openings as you move up higher in the building.
E N C L OS URE The various forms of diagram structures have been made possible through digital technologies that help us to conceive of and make visible complex three-dimensional constructions and compositions. Many of these creations would be difficult, if not impossible, to do by hand. This is especially true of the calculations necessary to determine the structural requirements for the individual members of a diagrid system.
Perimeter hoops resist the horizontal forces at each node level where the diagonal columns intersect. As with dome structures, the hoops in the upper region are in compression while those at the middle and lower levels are subject to significant tensile forces. The hoops also serve to transform the diagrid into a very stiff triangulated shell, freeing the interior core from the need to resist lateral wind forces.
The shape of the tower was partially influenced by the need to have a smooth flow of wind around the building and minimize its impact on the local wind environment. Across this curved surface the diagrid structure is formed by generating a pattern of intersecting diagonals spiraling in two directions.
Doors offer entry into a room and influence the patterns of movement and use within it. Windows allow light to penetrate the space and illuminate the surfaces of a room, offer views from the room to the exterior, establish visual relationships between the room and adjacent spaces, and provide for the natural ventilation of the space.
While these openings provide continuity with adjacent spaces, they can, depending on their size, number, and location, also begin to weaken the enclosure of the space. Along one edge Along two edges Turning a corner Grouped Skylight At Corners An opening can be located along one edge or at a corner of a wall or ceiling plane. In either case, the opening will be at a corner of a space.
Vertical Horizontal Three-quarter opening Window-wall Skylight Between Planes An opening can extend vertically between the floor and ceiling planes or horizontally between two wall planes.
It can grow in size to occupy an entire wall of a space. If centered within the plane, the opening will appear stable and visually organize the surface around it. Moving the opening off-center will create a degree of visual tension between the opening and the edges of the plane toward which it is moved.
The shape of the opening, if similar to the shape of the plane in which it is located, will create a redundant compositional pattern.
The shape or orientation of the opening may contrast with the enclosing plane to emphasize its individuality as a figure. The singularity of the opening may be visually reinforced with a heavy frame or articulated trimwork. Multiple openings may be clustered to form a unified composition within a plane, or be staggered or dispersed to create visual movement along the surface of the plane. As an opening within a plane increases in size, it will at some point cease to be a figure within an enclosing field and become instead a positive element in itself, a transparent plane bounded by a heavy frame.
Openings within planes naturally appear brighter than their adjacent surfaces. If the contrast in brightness along the edges of the openings becomes excessive, the surfaces can be illuminated by a second light source from within the space, or a deep-set opening can be formed to create illuminated surfaces between the opening and the surrounding plane. This directional effect may be desirable for compositional reasons, or the corner opening may be established to capture a desirable view or brighten a dark corner of a space.
A corner opening visually erodes the edges of the plane in which it is located and articulates the edge of the plane adjacent and perpendicular to it. The larger the opening, the weaker will be the definition of the corner.
If the opening were to turn the corner, the angle of the space would be implied rather than real and the spatial field would extend beyond its enclosing planes.
If openings are introduced between the enclosing planes at all four corners of a space, the individual identity of the planes will be reinforced and diagonal or pinwheel patterns of space, use, and movement will be encouraged. The light that enters a space through a corner opening washes the surface of the plane adjacent and perpendicular to the opening. This illuminated surface itself becomes a source of light and enhances the brightness of the space. The level of illumination can be enhanced further by turning the corner with the opening or adding a skylight above the opening.
If located at a corner, the vertical opening will erode the definition of the space and allow it to extend beyond the corner to the adjacent space. It will also allow incoming light to wash the surface of the wall plane perpendicular to it and articulate the primacy of that plane in the space. If allowed to turn the corner, the vertical opening will further erode the definition of the space, allow it to interlock with adjacent spaces, and emphasize the individuality of the enclosing planes.
A horizontal opening that extends across a wall plane will separate it into a number of horizontal layers. If the opening is not very deep, it will not erode the integrity of the wall plane. If, however, its depth increases to the point where it is greater than the bands above and below it, then the opening will become a positive element bounded at its top and bottom by heavy frames.
Turning a corner with a horizontal opening reinforces the horizontal layering of a space and broadens the panoramic view from within the space. If the opening continues around the space, it will visually lift the ceiling plane from the wall planes, isolate it, and give it a feeling of lightness.
Locating a linear skylight along the edge where a wall and ceiling plane meet allows incoming light to wash the surface of the wall, illuminate it, and enhance the brightness of the space. The form of the skylight can be manipulated to capture direct sunlight, indirect daylight, or a combination of both. If they are oriented to capture direct sunlight, sun- shading devices may be necessary to reduce glare and excessive heat gain within the space.
While a window-wall weakens the vertical boundaries of a space, it creates the potential for visually expanding the space beyond its physical boundaries. Living Room, Villa Mairea, Noormarkku, Finland, —, Alvar Aalto Combining a window-wall with a large skylight overhead creates a sun room or greenhouse space.
The boundaries between inside and outside, defined by the linear members of a frame, become obscure and tenuous.
The qualities of an architectural space, however, are much richer than what the diagrams are able to portray. The spatial qualities of form, proportion, scale, texture, light, and sound ultimately depend on the properties of the enclosure of a space. Our perception of these qualities is often a response to the combined effects of the properties encountered and is conditioned by culture, prior experiences, and personal interest or inclination.
Chapter 6 presents the issues of dimensions, proportion, and scale.
While the first part of this chapter outlines how basic configurations of linear and planar elements define volumes of space, this concluding section describes how the size, shape, and location of openings or voids within the enclosing forms of a space influence the following qualities of a room: From within a space, we see only the surface of a wall. It is this thin layer of material that forms the vertical boundary of the space.
The actual thickness of a wall plane can be revealed only along the edges of door and window openings. Openings lying wholly within the enclosing planes of a space do not weaken the edge definition nor the sense of closure of the space. The form of the space remains intact and perceptible. Openings located along the edges of the enclosing planes of a space visually weaken the corner boundaries of the volume.
While these openings erode the overall form of a space, they also promote its visual continuity and interaction with adjacent spaces. Openings between the enclosing planes of a space visually isolate the planes and articulate their individuality. As these openings increase in number and size, the space loses its sense of enclosure, becomes more diffuse, and begins to merge with adjacent spaces.
The visual emphasis is on the enclosing planes rather than the volume of space defined by the planes. As the luminous energy of the sun is dispersed by clouds, haze, and precipitation, it transmits the changing colors of the sky and the weather to the forms and surfaces it illuminates.
With the 12 Noon 2 PM shifting patterns of light, shade, and shadows that it creates, 4 PM the sun animates the space of the room, and articulates the 10 AM W forms within it. By its intensity and dispersion within the Sunset 6 PM room, the luminous energy of the sun can clarify the form of S the space or distort it.
The color and brilliance of sunlight can create a festive atmosphere within the room or a more diffuse 8 AM N daylight can instill within it a somber mood. The size of an opening in a wall or roof plane, however, is also regulated by factors other than light, such as the materials and construction of the wall or roof plane; code requirements for ventilation; the desire for views and visual privacy; the appropriate degree of enclosure for the space; and the effect of openings on the exterior form of a building.
The location and orientation of a window or skylight, therefore, can be more important than its size in determining the quality of daylight a room receives. An opening can be oriented to receive direct sunlight during certain portions of the day. Direct sunlight provides a high degree of illumination that is especially intense during midday hours. It creates sharp patterns of light and dark on the surfaces of a room and crisply articulates the forms within the space.
Possible detrimental effects of direct sunlight, such as glare and excessive heat gain, can be controlled by shading devices built into the form of the opening or provided by the foliage of nearby trees or adjacent structures. An opening can also be oriented away from direct sunlight and receive instead the diffuse, ambient light from the sky vault overhead. The sky vault is a beneficial source of daylight since it remains fairly constant, even on cloudy days, and can help to soften the harshness of direct sunlight and balance the light level within a space.
When located entirely within a wall plane, an opening can appear as a bright spot of light on a darker surface. This condition can induce glare if an excessive degree of contrast exists between the brightness of the opening and the darker surface surrounding it. The uncomfortable or debilitating glare caused by excessive brightness ratios between adjacent surfaces or areas in a room can be ameliorated by allowing daylight to enter the space from at least two directions.
When an opening is located along the edge of a wall or at the corner of a room, the daylight entering through it will wash the surface of the wall adjacent and perpendicular to the plane of the opening. This illuminated surface itself becomes a source of light and enhances the light level within the space. Additional factors influence the quality of light within a room. The shape and articulation of an opening is reflected in the shadow pattern cast by sunlight on the forms and surfaces of the room.
The color and texture of these forms and surfaces, in turn, affect their reflectivity and the ambient light level within the space. While some rooms have an internal focus, such as a fireplace, others have an outward orientation given to them by a view to the outdoors or an adjacent space.
Window and skylight openings provide this view and establish a visual relationship between a room and its surroundings. The size and location of these openings determine, of course, the nature of the outlook as well as the degree of visual privacy for an interior space. A long, narrow opening, whether vertical or horizontal, can not only separate two planes but also hint at what lies beyond.
A group of windows can be sequenced to fragment a scene and encourage movement within a space. As an opening expands, it opens up a room to a broad vista. The large scene can dominate a space or serve as a backdrop for the activities within it. A window can be located such that a specific view can be seen from only one position in a room.
Interior openings offer views from one space to another. An opening can be oriented upward to offer a view of treetops and the sky. A bay window can project a person into a scene. If large enough, the projected space can become an alcove able to be occupied. Tokonoma, the spiritual center of a traditional Japanese house Views should not be limited to the outdoors or adjacent spaces.
Interior design elements can also provide subjects for visual attention. A good house is a single thing, as well as a collection of many, and to make it requires a conceptual leap from the individual components to a vision of the whole. The choices … represent ways of assembling the parts. They can also make space, pattern, and outside domains. They dramatize the most elementary act which architecture has to perform. To make one plus one equal more than two, you must in doing any one thing you think important making rooms, putting them together, or fitting them to the land do something else that you think important as well make spaces to live, establish a meaningful pattern inside, or claim other realms outside.
Few buildings, however, consist of a solitary space. They are normally composed of a number of spaces which are related to one another by function, proximity, or a path of movement. This chapter lays out for study and discussion the basic ways the spaces of a building can be related to one another and organized into coherent patterns of form and space. Space within a Space A space may be contained within the volume of a larger space. Interlocking Spaces The field of a space may overlap the volume of another space.
Adjacent Spaces Two spaces may abut each other or share a common border. Spaces Linked by a Common Space Two spaces may rely on an intermediary space for their relationship. Visual and spatial continuity between the two spaces can be easily accommodated, but the smaller, contained space depends on the larger, enveloping space for its relationship to the exterior environment. In this type of spatial relationship, the larger, enveloping space serves as a three-dimensional field for the smaller space contained within it.
For this concept to be per- ceived, a clear differentiation in size is necessary between the two spaces. If the contained space were to increase in size, the larger space would begin to lose its impact as an enveloping form. If the contained space continued to grow, the residual space around it would become too com- pressed to serve as an enveloping space.
It would become instead merely a thin layer or skin around the contained space. The original notion would be destroyed. To endow itself with a higher attention-value, the contained space may share the form of the enveloping shape, but be oriented in a different manner. This would create a secondary grid and a set of dynamic, residual spaces within the larger space. Mathematics, form and function.
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Even if you are not into architecture and only into design or your an artist, this is a great book to have. It's got some amazing illustrations that are so beautiful to look at. I purchased not only the digital copy of this book but also the book copy of this. In an aritst perspective this is great to look at to see the basic structures of a building.