Geometry & Context - Nicole Bridges by Nicolebridges14

Geometry & Context

Contents Grid Planes Datum Representation Analysis Space Mass Datum Symmetry Transformation Structure

GEOMETRY

Notre Dame de Reims | Jean dâ&#x20AC;&#x2122;Orbais | 1345 | France

CONTEXT

Top: Giambattista Nolliâ&#x20AC;&#x2122;s | 1748 | Map of Rome

Contents

Concept Dialogue Space Program Order Environment Light Material Movement Scale Surface Color De-Familiarization Trope

GEOMETRY

Geometry, commonly known as a section of mathematics, houses many of the key principles of architecture. The principles that fall under geometry are all connected by the basics that make up geometry itself; grids, lines, points, shapes, etc. With these basic elements, geometry can be used to simplify the complex portions of an architectural piece. Geometry has been apart of architecture since the beginning of time. Basic forms and shapes being combined in additive and subtractive formations were and are used to create new shapes and forms. Geometry has also allowed for three-dimensional forms to be transfered onto paper as two-dimensional shapes, leading to the creation of more elaborate geometries. These geometries can be transformed and scaled, they can influence the experience that the space provides, they can accentuate a buildings features. Geometry is the shape of architecture.

â&#x20AC;&#x153;Architecture is geometry made visible in the same sense that music is number made audible.â&#x20AC;? - Claude F. Bragdon

GRID

The grid is one of the most fundamental aspects of geometry in architecture. The grid is composed of the most simple geometry, lines. Combining lines together with equidistant spacing in both the horizontal and vertical direction creates this grid. Because of its basic construction, the grid can be found in architecture from centuries ago. This is seen in the courtyard walls of the Ducal Palace, created in 1459. Using the grid, we can dissect the wall and the placement of all of its ornamentation. While the grid can be seen physically on the facade or other features, it can also be seen in the floor plan for many buildings such as the Observatory House by Tatiana Bilbao and Crown Hall by Dennic Villanueva. For these plans, the grid lines up almost perfectly with the structural supports of each building, sectioning each plan into a series of boxes that can be used to further dissect and analyze the building.

Observatory House | Tatiana Bilbao | 2008 | Mexico

Ducal Pa

alace | Luciano Laurana | 1459 | Italy

Crown Hall | Dennic Villanueva | 2014 | Chicago

PLANES

Like many of the other geometric principles, the plane is an element that is commonly associated with mathematics. In mathematics, the different planes represent different dimensions. This can also be applied to architecture. Major planes in architecture are usually quite easy to see, as they normally run perpendicular to each other. In John Hejukâ&#x20AC;&#x2122;s Wall House 2, you can physically see these planes as they are physically built as concrete walls. Fernando Tavoraâ&#x20AC;&#x2122;s Pousada de Santa Marinha does not have a concrete wall, but from the photograph on the right you can see where two major planes intersect. It is within these planes that we are able to add other geometric principles.

DATUM

Datum is a geometric concept that combines several others like an umbrella of sorts. A datum can be a line, a plane or a three-dimensional space which allows for it to incorporate other geometric principles such as grids, lines, horizon, and space. Datum is a reference point for which we view objects. It is known as a tie or an anchor that connects the other design elements. Datum allows for elements that are dissimilar to be grouped together and connected for easier comprehension and for organizational reasons. They act as the guides of these elements in this sense. For example, the photo of Auditorium Building in Chicago is taken where to planes meet at a corner, creating a two-point perspective. The Metro station on the other hand, has four planes meeting together to create a one-point perspective. Top: Auditorium Building | Adler and Sullivan | 1889 | Chicago Bottom: Mayakovskaya Metro station | Alexey Dushkin | 1938 | Russia

R EPRESENTATION

Sketch of Peter Zumthorâ&#x20AC;&#x2122;s Brother Klaus Field Chapel

Representation allows for translation of ideas. Creating diagrams both digital and physical can help to communicate the architectâ&#x20AC;&#x2122;s vision for a project. These diagrams contain geometries that can be interpreted and understood by engineers, contractors, and even other architects. In order to distinguish certain aspects of a drawing, designers may thicken the line weight. This caused that element to pop out amongst the rest. Representation can be seen in multiple forms including plan, section, elevation, and several others. These drawings can explain everything from structure and wall placement, to specific room use. Because they are drawings, representation is inherently geometric, combining lines to transfer ideas. Top: Crown Hall | Dennic Villanueva | 2014 | Chicago Bottom : Guggenheim Museum | Frank Lloyd Wright | 1939 | New York

ANALYSIS

Analysis is used across many subjects to break down complex concepts, making them easier to understand. This is the same for architecture. When looking at works of architecture, it is helpful to break down a buildingâ&#x20AC;&#x2122;s different features using analysis. Analysis uses the geometries and other aspects of a building to present its features and to draw attention or add emphasis. This can help people understand the structural system, circulation, and grid of the building, while also revealing different geometries and patterns within. For example, Observatory House by Tatiana Bilbao may seem complex at first glance, but when you use analysis to break it down you can see the clear geometries both in section and in plan.

Observatory House | Tatiana Bilbao | 2008 | Mexico ssss

SPACE

Space between pieces or components create different geometries that can be changed by rearranging the pieces. In architecture, these pieces can be the buildings themselves or the rooms/spaces within them. These spacial zones help to define the use of each space. Often times, the most used or populated areas will inhabit larger spaces or multiple spaces. These spaces can be easily seen by analyzing a plan or section of a building or other architectural work. A good example of this is Crown Hall by Dennic Villanueva where the bigger spaces are places that people inhabit for longer times, while the more private spaces like bathrooms are smaller in comparison. There are also times though, were the most important or sacred spaces are small and intimate. An example of this would be St. Peterâ&#x20AC;&#x2122;s Basilica which has many large geometric spaces, with small, sacred altars. Top: Crown Hall | Dennic Villanueva | 2014 | Chicago Bottom: St. Peterâ&#x20AC;&#x2122;s Basillica | Many | 1506 | Italy

MASS

Though mass is commonly associated with other science terms, it can also be applied to architecture. When many buildings are assembled, they can be thought of as a kit of parts, where you begin with one piece, and continue to add upon that piece with others. When dissecting a building, one can distinguish the main pieces of its exterior by looking at its mass. The massing of a building shows the geometric forms of the buildingâ&#x20AC;&#x2122;s exterior. A good example is the Denver Central Library by Michael Graves. The clear geometries of this building can be easy broken apart as separate masses, allowing for a deeper analysis of the building itself. Breaking apart the massing of this building also accentuates the three-dimensional geometric forms that it possesses.

Denver Central Library | Michael Graves | 1995 | Denver

SYMMETRY

Of all of the Geometric principles, symmetry is the easiest to spot and understand. Symmetry can be found in many of the other principles such as grid and mass, which make it easier for symmetry to be seen. While symmetry can be seen on a large scale like the form of the entire building or its facade, it can also be seen in the small details of architecture. To achieve the appearance of perfect symmetry, many architects will alter their designs in a certain way in order to correct for the natural curvature of the human eye. A historic example of this is the Parthenon whose architects used small asymmetries to make the temple appear perfectly symmetrical. Other buildings like the Louvre Museum in Paris, France have symmetry in that they are composed of all identical sides.

TRANSFORMATION

ORIGINAL Transformation is a way of improving upon ideas. Transforming previously established building styles can result in a completely new style. Continuing to transform something more than once creates diversity in architecture. This is because transformation alters the geometry of what it acts upon, created new shapes and forms that can be used to improve everyday life. Without transformation, we would evolve at a much slower rate and all of our buildings would look the same. Transformation does not mean to completely change what was already there. One change being made could be considered transformation, leaving the product looking similar to the original. On the other hand, Transformation can develop something that does not resemble the original at all. Either way, Transformation, big or small, make an impact in pushing forward the evolution of Architecture by creating new geometries.

TRANSFORMATION: SPLIT

TRANSFORMATION: SPLIT + PINCH

STRUCTURE

While structure is what keeps the building standing, it can also create geometries within the building. For example, the walls of a building create the buildingâ&#x20AC;&#x2122;s shape on the outside, while dividing and creating smaller spaces on the inside. These smaller spaces may all be the same or different depending on the architectâ&#x20AC;&#x2122;s vision. In this case, these spaces create different geometries and experiences within the building. If the building has columns, they likely come together to form an underlying grid within the building. In many cases, certain geometries, such as the triangle, are considered more stable than others. Both of the buildings on the right use a triangular shape in order to keep their structures sturdy and stable.

When an Architectural work is created, it does not exist on its own. Architects must consider the context of the site that it will inhabit. This context is how the work will interact with those around it and the people within the surrounding area. This relationship can be positive or negative, it can change the way that people view things that have become metonymy. Context also controls the experience that is had within an architectural work. By arranging spaces and controlling movement throughout a building, it is possible to create completely different experiences for different people. Context is important because it allows works to mesh well with those around them, because without context, many buildings would be built without regard for cultural or environmental restraints making them more likely to fall or cause a negative reaction among the general public. Considering context when creating architecture is mandatory because buildings will only stand until they are knocked down.

â&#x20AC;&#x153;As an architect you design for the present, with an awareness of the past, for a future which is essentially unknown.â&#x20AC;? â&#x20AC;&#x201C; Norman Foster

CONTEXT

CONCEPT

Concept is the beginning of the entire design process. A concept provides a base for context, within a concept, the designer is deciding how to purpose a space. To do this, designers or architects will draw a series of sketches and diagrams in order to get their ideas on paper for further development. To develop a concept, they will take into consideration the context for which the building will stand. This is likely the climate, site location, site density, light distribution and a number of other factors.

Top: Dune House | Jarmund/VigsnĂŚs Architects | 2011 | Norway Bottom: Concept Sketch for Dune House

DIALOGUE

In the English language, dialogue is a term used to refer to a conversation that is had between people, this also applies to architecture. When multiple people view a work of art, and likewise, a work of architecture, they each provide a different perspective based the different experiences that they have had throughout their life. Because of this, architecture and those alike, are constantly evoking different interpretations from those of different cultural contexts. An example of this is the Vietnam Veterans Memorial Wall in Washington D.C.. This wall was interpreted as a mirror, a gravestone, and much more, all depending on who viewed the piece. Dialogue can also be between buildings. A good example of this are Borromini’s Oratory of the Filippini and the Chiesa who both share many similarities in facade, causing those who pass to refer to one of them when describing the other. Dialogue is rooted deep in the context of the viewers mind and of the site’s history.

SPACE

In the last section, we talked about the geometric aspects of space. Space is also, however, very important when defining context as well. Though the shapes of a space define the inward experience of the entire building, the way that the spaces interact with each other is contextual in its roots. For example, placing the dining room next to the kitchen is contextual because of how both of those spaces are used. Another example would be building placement within a city. Within cities there are perceptual zones that are used to group and categorize cites. These zones can be cultural, income-based, or based on how the spaces are used like in the kitchen example. The maps to the left both involve this building placement and spacing. The Greek Acropolis was built to allow all of the buildings to be viewed at once, and spaced accordingly. The Map of Rome emphasizes the spacing of Rome with dark elements, showing the literal context of spacing within the city.

Top: Giambattista Nolli’s | 1748 | Map of Rome Bottom: Constantinos Doxiadis’ | Acropolis Drawing

PROGRAM

The program of an architectural work is different based on the intended use for that work. Once the use for a building is decided, it is then easier to decide what the building will look like on both the interior and exterior. Program is a list of requirements, usually set by the architect and client, placing designated spaces near each other in order for the building to flow well, without lacking any one part.. An example of program would be placing all of the bathrooms of the building near each other, allowing the plumbing to reach all of the spaces without creating multiple plumbing hubs. You can see this in the floor plan for Crown Hall, whose program places both bathrooms strategically near each other. Another example would be a greenhouse versus a regular house. A green house is designed to allow in sunlight and heat without allowing it to escape. Greenhouses such as the Barbican Conservatory allow for plants to thrive in an area that does not support their normal living conditions. A normal house is for humans to inhabit and usually uses central heating and cooling to create an adjustable temperature. Program can even dictate color and material uses in buildings.

ORDER

Order is how spaces are placed relative to other spaces. Order is important in curating the experience of an architectural work. In VitraHaus, the architects use repetition to stack spaces nonorthogonal to each other. This provides the visitor with a sense of familiarity when moving throughout the building because the spaces are the same, but the furniture is different. In the Mother House of the Dominican Sisters, the architect has contrasted rectilinear forms with organic forms in order to create the floor plan. The spaces in the center are place nonorthogonal to each other while being encased in by the outer rooms. The use of order within architecture impacts the entire experience of a building.

ENVIRONMENT

Environment is one of the biggest influences of architecture. Environment dictates the materials, structure, and even the space itself. Places that are earthquake prone cannot construct buildings in the same way that one would construct in a humid, tropical climate. Along with climate, it is also important to consider the type of lighting, whether it is diffuse of direct, or itâ&#x20AC;&#x2122;s harshness. In places where the light is more gentle, they will likely allow the maximum amount of natural light and vice versa for harsher lighting. If people did not consider their Environment when building, many of these buildings would fall frequently, becoming a safety hazard for those that live near and around them. Torre Reforma has taken into account the seismic activity in Mexico City and has been made with special materials in order to withstand the frequent earthquakes. The Nisser Micro Cabin is built near water, so it has stilts to account for the rise and fall of the water. Each building takes Environment into account to a certain extent, basing everything from building styles, to material on climate context.

LIGHT

Light can change the experience that a space provides. The way that light enters a space can have both practical and symbolic implications. For example, The Church of Light in Osaka, Japan shapes the light entering the building into a cross, an important symbol to the Christian faith. This both draws attention to and helps to emphasize the importance to this symbol. Practically, light is used for seeing. In the Exeter Library in New Hampshire, this is definitely the case. Here, they have used the way that light enters the space to light each work space without need for artificial light during the day. The way that light bounces off of surfaces is taken into consideration when creating spaces because it can change the way that the space is perceived and what its functions are. For example, people tend to work in well lit spaces because they need to see what they are doing. Places such as churches or theaters can be dimly lit because of the activities that take place there.

MATERIAL

A buildings material composition can be influenced by a number of contextual factors. Climate, use, and culture are a few of these factors. Buildings in a warmer climate are built in order to allow air flow within and to keep the sun out. Dominus Winery in Napa, California uses rocks stacked between two walls of fence to achieve this. The mix-matched fit of the rocks allows the wind to get through, while keeping the majority of the sun out. When it comes to the intended use of a building, there are many materials that are better suited for a task than others. For example, Tokyo Opera City by Tokohiko Yanagisawa is a music hall whose interior is crafted completely out of wood. Wood is good at reflecting sound which would allow the performers to be heard well from any seat in the music hall.

MOVEMENT

Movement dictates the experience of a space. How people move through a space impacts their interpretation and experience within that space and those in its surrounding area. Certain buildings like the Guggenheim Museum in New York have only one circulation, forcing the visitors to experience each space in a particular order, modifying their experience. This is known a sequence, an integral part of movement which dictates how people interact with each space. Other buildings allow people to choose different ways to move between two of the same spaces. An example of this is SESC Pompeia by Lina Bo v which uses forked bridges to allow people to choose which side they would like to enter the space. Some buildings may have multiple sequences for different types of people such as a courthouse which has different movements for spectators, the judge, the jury, etc. The spaces of a building are static, but moving through them allows for them to be connected and experienced in an entirely different way.

SCALE

Scale, in general terms, is how big something is relative to something else. Without context, scale is not very helpful. For example, a leaf may be large when compared to an ant, but that same leaf is minuscule when compared to the tree that it fell from. As with anything else, the scale of a building is relative and it can even change as one moves throughout a space. Moving through the space creates new references for scale as one loses sight of one object and is presented with others. For example, from a top view, it is easy to tell that the wooden blocks are all the same size; however, when you view the blocks from the front it seems like the block in the front is bigger than all of the rest. This is one instance in how movement can influence scale. Once other pieces are added, it is easier to see the scale of the blocks because now there is more to referent their size to. The scale of an object is contextual and it depends on the reference of another object nearby.

SURFACE

The surface of a building is the first thing that is seen from far away. A building’s surface is so important that many decorate building’s in intense ornamentation in order to reflect the richness of the interior. The surface of a building is how the building’s interior interacts with the exterior, it blends the two together while also giving them separation. Considering context is very important when creating the surface of a building. In some cases, architects want to inspire change by allowing their building to stick out like the Ftown building, a white, patterned building surrounded by gray concrete buildings. Others want their building to blend seamlessly into the landscape and appear natural to its environment. A good example is Palazzo Canossa in Verona which was built in 1526 in order to unite a portion of the street that a wealthy family had recently acquired. Top: Palazzo Canossa | Michele Sanmicheli | 1526 | Italy Bottom: Ftown | Atelier Hitoshi Abe | 2006 | Japan

COLOR

The color of an architecture work can affect how that work fits within the context of its surroundings. Color can help to connect a group of objects. The colors associated with these objects have international meaning such as the color red, which means to stop or that there is danger ahead, and the color yellow, which means caution. Along with external meanings, color can also be used to blend buildings together or allow certain elements to stand out. In order to make elements stand out, designers often stick to a certain color scheme in order to make the colors of the elements pop and compliment each other. For example, Luis BarragĂĄnâ&#x20AC;&#x2122;s Casa Gilardi uses a tertiary color scheme to emphasize the different elements.

Top: Casa Gilardi | Luis Barragรกn|1976 | Mexico Bottom: Brownstone Houses | San Fransico

DE-FAMILIARIZATION

In the world of architecture, there is often a misconception that buildings only provide shelter from the elements. Though this is true buildings also provide a place for daily activities, adding a sense of comfort when we see certain types of buildings. For example, many people are able to look a county jail and tell its purpose based on its design. This sense of comfort allows for people to associate certain building types with certain purposes, making it hard for many to â&#x20AC;&#x153;think outside of the boxâ&#x20AC;? in terms of the designs and layouts for these building types. Though it may not be as helpful in this case, decomposition can allow people to take a new look at what is around them. Rearranging the pieces of a building gives it an entirely new context. This is seen in the decomposition here on the right. The M2 building in Japan has many pieces that fit together and create an interesting building. Decomposing the building helps to not only recognize these pieces individually, but also experience the building in a new light. M2 Building | Kengo Kuma | 1991 | Japan

TROPE

Like De-familiarization, Tropes are also used to encourage a fresh view on the things that have become conventional. This can be by associating works of architecture with metaphors or similes. An example of this is the TWA flight center at JFK airport in New York. Many believe that the airport looks like a bird or a plane due to its largely spread, wing-like structure. Another way to employ tropes is through exaggeration or hyperbole. This will usually occur when the architect or designers wishes to emphasize a certain featureâ&#x20AC;&#x2122;s uniqueness. A good example of this is the M2 building in Japan by Kengo Kuma. The large Greek column at the center of the building is already quite strange in an Asian country, but instead of hiding this feature, Kuma enlarges it to emphasize its uniqueness in the context of its city. Tropes can also be described as being either a duck or a decorated shed. The duck emphasizes the main aspect of the building on the exterior. The decorated shed expresses one aspect on the outside that does not match the inside. This helps to break the metonymy of how people view buildings that have become conventional.