Chapter 6

Proportion and Scale

The Golden section is a scale relationship between two dimensions of a plane or line , in which the equation of the lesser to the greater is the same as the greater to the whole: a quotient of 0.618 to 1.000.  This mathmatical eqaution began with the Pythagorean idea that numerical relationships bring unity to the universe.  Greeks believed that the Golden Section was visible in the human body, therefore, buildings that housed the body should have the same proportionate balance. 

The Golden Section may be written as an algebraic equation 

 a  =  b                                                                                                           

 b    a+b

The Golden section is similar to the Fibonacci series where each tern is reached by the sum of the preceding two numbers:  1, 1, 2, 3, 5, 8, 13.....

A Golden rectangle may be formed using the theory of the Golden section and may be carried out indefinently with each section remaining in a similar relationship to all other parts as well as the figure as a whole.

The Orders of classical Roman and Greek architicture represented forms the contained both consistancy and elegance.  Measurments were based on the circumference of the column.  Everything down to the smallest details of the building were determined by the columns and their spacing.  The order are:  Tuscan, Doric, Ionic, Corinthian and Composite.                          The order of Temples by intercolumniation, diameter, height and spacing of columns :  Pycnostyle,  Systyle,  Eustyle,  Diastyle and  Araeostyle.

The architects of the Renaissance Theories believed that their designs were part of a greater plan.  They also used the Greek classification of scale.  The renaissance gave birth to an infinite advancement of numerical scales that was the foundation of their building.  Renaissance architect Andrea Palladio suggested that there are seven "beautiful and proportionable" scales for rooms:  circle, square, 1: 2,  3:4,  2:3,  3:5 and 1:2.  Palladio also developed equations to determine the appropriate ceiling size.  Flat ceilings were equal to the rooms width.  Vaulted ceilings in square rooms were one-third greater than their width.  For other rooms the Pythagoras' theory was used to regulate the ceiling heights.  This was a theory that used math, geometry and harmony.

The Modulor is a system of proportions determined by LeCorbusier.  He based this modulor system of order on both the Golden Section and the Fibonacci Series, as well as the dimensions of the human form.  His scale contained three measurements based on the human body: 113 cm, 70 cm and 43 cm.

The Ken is a method of measurment developed during Japan's Middle-Ages. The ken is used to determine the construction, materials, space and order of a building.  In Japan, the diameter of a room is calculated based on size of the floor mats (3 x 6 shaku or 0.5 x 1 ken).  Floor mats have become a standard measurement for floor systems and column width.

Anthropometry is a scale of measurement based on the size and scale of the human body.  This theory states that architecture is an continuation of humanity and should be compatable to the body's shape and form.  Anthropometry must factor in changes in the body due to differences in sex, race and age.  Ergonomics is the science that deals with the design of gadgets and surroundings and how they work with the human body. 

Proportions are also determined by visual and human scales.  Visual scale is the reference of how large or small a structure is comapared to the standard size of the object ( small or large). Visually, it is how design elements are seen and how they related to one another individuallyand as a whole. The human scale is determined by the measurements and scale of a human body.  Scale in relation to our body can determine how we feel in that space.  The height of the ceiling in a room has the strongest effect on a rooms scale.  Other factors that alter the scale of a room include: color, pattern and shape of the facade,                                                                        placement, size and order of openings,                                                                                                     the proportion and essence of items placed in the room.

Chapter 5

Circulation

Building Approach is the preception of a building from a distance.  The approach to a building may vary in distance, view, and continuity with the surrounding enviroment.  The entance may be frontal, oblique or spiral.  

A frontal approach guides us along a direct, paramount lane.  This lane has a clear end, the entrance of the building.  

An oblique approach plays off the vantage point of the vaneer and the entire form of the building.  An oblique lane of enrty may by redirected numerous times in order to enhance the experience of entering the building.  

A spiral entry exaggerates the approach of the building so that we may experience the formand space from all angles.  As the lane of entry leads around the perimeter of the building, the entrance may be viewed at different points during the approach or it my remain obscured until the end.

Building entrances are the transition from the exterior to the interior of a building.  The act of entering requires a perpendicular structure that defines one space from another. An entrance may be as simple as a hole in a wall, a beam and pillars , or a threshold; or it may be complex and elaborate.  

Entrances are arranged into three groups:  flush, projected and recessed.  A flush entry is a cohesion of the exterior wall.  A projected entry constructs a variable space that provides overhead coverage to the entry way.  A recessed entry also provides shelter as in carves the  entrance into the buildings form.  Entry ways may be a preview of the space about to be entered or may be unique to the space in order to underscore the the seperation of the exterior and interior space.

The entrance may be visually enhanced by making the entryway opening lower, wider or narrower the expected.  The entrance may also be enhanced if it is meandering or deep.  Many times the entrance of a building is distinguished by an embellished entry ways.

Configuration of the path is a linear avenue with ab distinct beginning that directs through a series of spaces to a destination. The delineation of the path is determined by the way and manner in which the path will be followed.  ie: pedestrian, cyclist, cars etc.  

The traverse of two or more paths give the traveler a point at which alternative routes may be explored.  The continuance  and proportion of the path helps differentiate major routes and spaces from minor routes and spaces.  The nature of composition and structure of a path is both determined by and determines the organization of spaces and forms that it brings together.  

All paths are linear in nature.  These linear paths may take on the nature of being curved or segmented, having interchanges, with various branches and hoops. 

A radial path leads to or from a pivotal site in the space.

A spiral path is one path that begins at a central point and orbits out at increasing intervals.

A grid path is made up of two parallell lines that cross in consistant sequences forming a geometric pattern of square shapes.  

A network path is made up of serveral different trails that lead to and bring together different points in a field.

Building spaces generally use a  composite or combination of these path configurations.  A stratified system of paths , building forms and spaces are created and emphasized by varying placement, shapes, size and span .

Path-Space relationship may be translated in three ways:  pass by spaces, pass through spaces and terminate in a space. 

Pass by spaces preserve the individaulity of each space.  The contour of the path traveled is adjustable.  Arbitrary spaces may be placed along the joining path. 

Pass through spaces do just that, they literally pass through a space at a given point. By passing through the space different patterns of flow and shift are created in the form.

In the terminate in a space, the emphasized space determines the path to be followed.  The path established leads directly to and ends at the entrance of the determined space.

The form of circulation space is designed to entertain the flow of people in a location. The form of circulation space changes based on: the defined space; how the space relates to the joining spaces;  the nature of light, size, scale, and perspective; various entrances; various levels in the spaces linked by stairways and ramps.

The form of a circulation space may be enclosed completely, open on one side or open on both sides.  The size and scale of a circulation space is determined by the amount of travel that it must handle.  A tight path urges forward movement.  This space is expaneded to encourage stopping and observing the space.  An expansive space may have no pre-determined path, but the movement may be altered by the activities taking place or an adjustment of accessories in the space.

Stairways allow for movement between levels of a space. A stairwell should be broad enough to allow for easy passage.  The height and width of stairs vary according to the nature and purpose of the building.  Landing provide a break in the stairs which allow for a pause or change in movement.  Stairs are designed to allow for a change in level, movement or course of travel. There are five main configurations of stairways: straight run, L-shaped, U-shaped, circularand spiral.

Stairways may be carved into the design of a building as a volumetric solid. They may wrap around the edge of a space.  Stairs may be placed in a thin uninviting shaft between walls or have large steps that spill out from large inviting landings.  Stairways are three-dimensional structures that may appear as a freestanding or fixed sculpture in a room. 

Chapter IV

Spatial Relationships:

Space within a space is when a smaller space is within the boundaries of a larger space.  Perceptual and structural harmony can exist between the two spaces , however, the lesser space's relationship to the exterior is contingent on the larger space.

The size and integrity of the two spaces is dependent on each other. The relationship between the two spaces changes if either space increases or decreases in size.

The space is made more interesting by the inner structure. The two spaces may share the same shape but the outer space becomes more dramatic if the inner space is set in a different direction. Or the inner structure may take a different shape building on the importance and difference of each individual space.

Interlocking Space is when two individual structures are merged together and share a common space.  Each space remains separate, however the married space may be defined in different ways:

The joined space may share the same volume of each structure.

The joined space may merge completely into one of the structures.

The joined space may become independent of the two original structures.

Adjacent space is when a common border joins two individual structures. This is the most common relationship between two spaces.  Each space remains independent in its form and function.  The plane that both separates and joins the forms determines the relationship between the spaces.

The plane that separates the forms allows limited access between the structures re-enforcing the structural integrity and individuality of each space.  The adjacent spaces may appear as one freestanding structure.  In some cases, the space may be divided by  a row of columns which allows for the separate spaces that appear as one.   The spaces may also be divided by a change in height, material or texture; the spaces may appear as one single structure divided by some form of change. 

Spaces linked by a common space.  Two independent structures may be related and joined by a third structure.  This third, intermediate space, determines the visual and spacial relationship between the entire structure.  The third space may vary in orientation and structure.  All three spaces may be equal in size, shape and space.  The third space may become linear to link the two independent spaces.  The third space may be a large enough to become the dominant space or it may be a secondary structure with its shape determined by the two spaces being joined.

Spatial organizations

Centralized organization contains a number of secondary spaces formed around a dominant space in the center of the structure.  The central space is generally a large regular shape.  The secondary shapes may be equal in size and form creating a symmetrical, geometric structure; or they may be in different size and form meeting individual requirements of the structure. 

Centrally organized structures are non-directional; therefore, an entry must be specified. 

A centrally organized structure may have varying forms of movement (spiral, radial or loop) which all come to an end in the central space.

A central organization may be interior or exterior space.

Linear organization is a series of structures that are directly related by individual linear spaces around them.  Linear organization is generally made up by repeating spaces.  Each structure in the sequence has an exterior exposure.  Although, structures of importance may occur anywhere in the sequence, they are sometimes placed in a sequential location that emphasizes their importance. ie. the end of a sequence, a sequence pivot point or off set from the sequence.  Structures of importance placed in the sequence often vary in size or form.

Linear organization is used to express direction, movement and growth.  Linear organization leads to another space, form or entrance. Linear organization has endless possibilities and can adopt to the surrounding environment.  Linear organization can bring together and organize other forms, serve as a barrier to separate forms, or enclose forms in a limited space.

Radial organization brings together central and linear organization by having a central space from which several linear spaces emerge.  The radial arms are capable of reaching out and linking together distinct spaces and structures.  The center of a radial is generally a regular shape  while the arms may vary in order to meet specific form and function. 

Clustered organization does not depend on a regular geometric shape, therefore, it is flexible and can grow without disrupting the integrity of the design.  Clusters depend on physical location to relate the spaces to one another.  Clusters may be organized on repetitive spaces, common shapes or a common axis.  They may be grouped around an entry way, a pathway or to form a loop.  A cluster may be organized around a central pattern, a clustered pattern or a contained space.  Size, form and orientation dictate importance within a cluster because there is no one place of importance.  A cluster may be unified and better organized by the use of symmetry or a axis.

Grid organization is determined by a three dimensional grid pattern.  It is a structure of repetitive space and pattern that forms the skeleton on which a structure is formed.  A grid may be added to, subtracted from or layered on in order to define the space and allow a space to grow or adapt to the surrounding area.  A grid may undergo countless changes on order to make the  necessary adjustments in a form.