Download Beyond the Façade - Department of Mathematics

Contents
1. An Introduction to Architecture and Geometry
2
2. The Basics Forms and the Methods of Application
3
3. The Early Years
13
4. La Belle Époque and Sacred Mathematics
15
5. Art Deco and Geometry Galore
21
6. A Call to Disorder and Giant Geometry
27
7. The Geodesic Dome
34
8. Bibliography
36
1
Introduction
1.
Architecture and geometry are symbiotic in nature, virtually an inseparable pair.
Understanding the principles of lines, planes, solids, patterns and surfaces are integral to
the architect’s design concept. Regardless of the magnitude of the project, be it the
construction of the St. Peter’s Basilica or a nondescript factory plant, the architect’s
understanding of geometry is crucial. On the other hand, if geometry is not employed by
architects, the understanding of the subject would merely be a scholarly exercise. The
knowledge of geometric principles by the architect empowers him to use geometry as an
instrument to realize his creativity. A balance of the science and the artistic would result
in the erection of many structures of great beauty that would enhance our quality of life.
The amalgamation of geometry and architectural design is evident throughout
history. The angles of inclination of the walls of the Egyptian pyramids were determined
4600 years ago by a geometric construction. Even today, geometry is used to great effect
with modern and abstract constructions such as the Guggenheim New York, consisting of
a symphony of triangles, circles and arcs.
This project is not one that charts the development of Singapore architecture.
Rather, it is a project that explores the different relationships between geometry and
architecture in Singapore since 1819. Through the course of this project, we have also
discovered an interesting trend towards an increase in the amount of geometry being
incorporated into modern buildings, resulting in an interesting blend of the traditional and
the avant-garde.
It is hoped that this project will help make readers be more alert of their
surroundings and not merely see buildings as blocks of steel, glass or concrete but think
of them as machines that have been put together by many simple elements.
2
2.
The Basics Forms and the Methods of Application
“Cubes, cones, spheres, cylinders or pyramids are the great primary forms that
light revels to advantage, the image of these are distinct and without ambiguity. It is
for this reason that these are beautiful forms.”
2.1
Le Corbusier1
An introduction to the Primary Solids 2
Any building, no many how sophisticated the design, is made up of primary shapes that
have been cleverly put together. Primary solids are the building blocks of the world. The
primary shapes can be extended or rotated to generate volumetric forms or solids which
are distinct, regular and easily recognizable. Circles generate spheres and cylinders;
triangles generate cones and pyramids,; squares generate cubes. In this context, the term
solid does not refer to firmness of substance but rather to a three-dimensional geometric
figure.
The Cube
A prismatic solid bounded by 6 equal square
sides, the angle between any 2 adjacent faces
being a right angle. Because of the equality of its
dimensions, the cube is a static form that lacks
apparent movement or direction. It is a stable
form unless it stands on one of its corners or
edges. Even though its angular profile is affected
by out point of view, the cube remains a highly
recognizable form.
1
2
Frank D.K. Ching, Architecture, form, space & order, (New York : Van Nostrand Reinhold) , 1996, p 42
Ibid, pp 42-43.
3
The Pryamid
A polyhedron having a polygonal base and
triangle faces meeting at a common point called
a vertex. The pyramid has properties similar to
those of a cone. Since all of its surfaces are flat
planes, the pyramid can rest in a stable manner
on any of its faces. While the cone is considered
a soft form, the pyramid is relatively hard and
angular.
The Sphere
A solid generated whose surface is at all
points equidistant from the centre. A sphere
retains its circular shape when viewed from
any angle. It is generally stable in its
environment unless a force has been applied
to it or when it is placed on an incline plane.
The Cylinder
A solid generated by the revolution of a
rectangle about one of its sides. A cylinder is
centralized about the axis that passes through
the centres of its 2 circular faces. Along this
axis, it can be easily extended. The cylinder
is stable only when it rests on its circular
ends and becomes unstable when its central
axis is parallel to the horizontal plane.
The Cone
A solid generated by the revolution of a right
angle triangle about one of its sides, like the
cylinder, the cone is highly stable when
resting on its circular base and unstable when
its vertical axis is not perpendicular to the
horizontal.
4
2.2
Transformation of Form
All other forms can be understood to be transformation of primary solids, variations
which are generated by the manipulation of one or more dimensions or by
adding/subtracting elements.
i. Dimensional transformation
A form can be transformed by altering one or more of its dimensions and still retain its
identity as a member or a family of forms. A cube, for example, can be transformed into
similar prismatic forms through discreet changes in length, width or height. It can be
compressed into a planer form or be stretched out to a linear one (refer to sketch below).
As seem in the picture above, the Raffles City Tower, designed by I M Pei in 1985, is in
fact essentially an elongated cube when we disregard the chamfered edges.
ii.
Subtractive transformation (Truncation)
A form can be transformed by subtracting a portion of its volume. Depending on the
extent of the subtractive process, the form can retain its initial identity or be transformed
into a form of another family. For example, a cube can retain its original identity as a
5
cube even though a portion of it is removed, or be transformed into a series of regular
polyhedrons that begin to approximate a sphere (refer to sketch below).
An example of this process of truncation that alters the original form of a shape is
displayed by the Republic Plaza which is found at Raffles Place. While it has been built
on a relatively square base, the edges of this square base have been pared off to give the
tower an octagonal look.
iii.
Additive transformation
A form can be transformed by the addition of elements to its volume. The nature of the
additive process and the number and relative sizes of the elements being attached
determine whether the identity of the initial form is altered or retained (refer to sketch
below)
6
The Supreme Court at City Hall3
Front Elevation
The Supreme Court that was completed at the edge of the Padang in 1939 is an excellent
example of addictive transformation. The main building, a rectangular block/ prism, has
been added with the various primary shapes such as the square and the semi-circle (refer
to sketch above). The main building achieves harmonious balance and symmetry with the
the portico capped by a tympanum, which in this case is a isosceles triangle.
The main building is capped off by another classical element, that of a geodesic dome.
Modelled after the St. Paul’s Cathedral in London, the dome is perched above 2 levels in
what seems like a pavilion. The use of the pavilion to elevate the dome, is perhaps to
prevent the tympanum from obscuring the view of the dome, the crowning glory of
Victorian architecture.4
The axis of symmetry in this case would then by the apex of the tympanum, through the
building. When we see it as the axis of symmetry, we can see then, that each “dissected”
side of the building would then map onto the other perfectly.
iv. Subtraction form
We search for regularity and continuity in the forms we see within our field of vision. If
any of the primary solids is partially hidden from our view, we tend to complete its form
3
4
Photo taken from the Online Photo Archives of the National Heritage Board, http://picas.nhb.gov.sg
Gretchen, Liu, In Granite and Chunam, (Singapore, Landmark Books), 1995, pp. 70 -80.
7
and visualize it as if it were a whole because the mind fills in what the eyes do not see. In
a similar manner, when regular forms have fragments missing from volumes, they retain
their former identities if we perceive them as incomplete wholes if we refer to these
mutilated forms as subjective forms.
Because they are easily recognizable, simple geometric forms such as primary solids,
adapt readily to subtractive treatment. These forms will retain their former identities if
portions of their volumes are removed without deteriorating their edges, corners and
overall profiles.
“A building is the only thing that can make land pay.”
Louis Sullivan
Maybank Building, Singapore headquarters of the Malaysian Banking Corporation
at Fullerton Square (completed in 1998)
View of Maybank Tower as viewed from the sea
Rearview of Maybank
As the office tower of Maybank is located on a very narrow plot of land (refer to picture
on the right), the architect has designed the building to resemble the spinnaker of a sail
8
boat so as to create an optical illusion that makes the building look visually larger/wider
than it really is when viewed from a specific angle (refer to picture on the left).
The building is built on a relatively broad base but gradually tapers inwards to meet the
apex. This creates a visual effect that makes the building appear to be an octagon like
when one views the office block in front of the Fullerton Hotel as seen in the picture on
the left.
The alternating narrow bands of blue glass and beige granite also help
emphasize the horizontal.
Maybank Tower has shown that the number of surfaces that can be viewed from a
particular angle can actually give the false impression of a building’s actual size.
An interesting comparison with the Maybank Building:
The office block of Raffles City on the right (designed by I M Pei in 1988) is shaped like
a truncated and elongated cube unlike Maybank Building whose shape skillfully hides its
inadequate dimensions.
9
Shaw House at Scotts Rd
Winsland House at Killiney Rd
Spatial volumes may be subtracted from a form to create recessed entrances positive
courtyard spaces (Shaw House), window openings shaded by the vertical and horizontal
surfaces of the recess. For example, a large square recessed area has been made on the
curved corner of the façade of Winsland House, however, this has no effect in altering
our overall perception when recognizing the façade in fact curved.
Ambiguity regarding the original identity of a form will only result if the portion
removed from its volume erodes it edges and drastically alters its profile.
10
2.3
Symmetry
Symmetry is the balanced distribution and arrangement of equivalent forms and spaces
on opposite sides of a dividing line or plane, or about a centre of axis.
There are two fundamental types of symmetry:
1. Bilateral Symmetry
Refers to the balanced arrangement of similar or equivalent elements on opposite
sides of an axis so that only one plane can divide the whole into essentially identical
halves.
A common feature of classical architecture is the vertical symmetry
possessed by
the structure. The Fullerton Hotel constructed in 1929 at the mouth of the Singapore
River, has vertical symmetry. The red line bisects the building into 2 identical halves.
This symmetry is further emphasized by the use of roman columns. The use of
columns gives the illusion of a “perfect balance” to the building.
5
5
Picture taken from the official Fullerton Hotel website at www.fullertonhotel.com
11
2. Radial Symmetry
Refers to the balanced arrangement of similar, radiating elements such as the
composition can be divided into similar halves. By passing a plane at more than one
angle around a centre point or along a central axis.
6
Above is a photo of the Telok Ayer Market at Shenton Way which was constructed in
1894. The market is in the shape of an octagon with the central clock tower as the
centre point of the structure. When one draws any straight line from any corner of the
octagon and pass through the clock tower, this line will divide the structure into 2
similar halves.
6
Photo taken from Helmer Aslaksen’s “ Mathematics in Art and Architecture” website at
http://www.math.nus.edu.sg/aslaksen/teaching/maa/Symmetry_in_Art_and_Architecture.ppt
12
3.
The Early Years
Singapore in the 19th century was characterized by mainly low-rise buildings no higher
than 2 storeys as Singapore. The island had a relatively small population and spraling
gardens that surrounded the house was not considered a luxury. Buildings were kept
simple in design low due to the low level of engineering technology as well as the lack of
building materials.
Colonial Bungalows
House at No 2 Cable Rd (circa 1870s)
Early “Black and White” colonial bungalows shown above are classic examples of the
use of additive transformation. The main building is essentially a cube. The porch has
been added perpendicularly to the northern corner of the main building. The jack roof
(turret) is also another square which is placed parallel to the porch. This extension of the
building alters the façade of the building, but the original form of the main structure (the
square) can still be discerned.
Also note the vertical symmetry of the building. The located of window on both sides of
the house is almost symmetrical.
13
House at Jervois Rd ( circa 1870s)
The bungalow at Jervois Road is similar to the bungalow at Cable Road. With a cube as
the a main portion, the intended front of the house has been extended through the use of
additive transformation. The introduction of a rectangular block, produces a porch area.
As with most traditional architecture, this building too, possesses vertical symmetry.
14
4.
La Belle Époque and Sacred Mathematics
By the end of the 19th century, Singapore became the capital of British Malaya. The
increase in the level of prosperity is reflected in the construction of numerous elaborate
and ornate buildings from 1890 to the outbreak of WWII. While these buildings may only
seem well designed to the layman, they are also rich in sacred numerology and many
mathematical references may be observed.
4.1
East Meets West
Bungalow along Mountbatten Road built in the early 20th century
The bungalow is essentially made up of a square main block with an octagonal prism
added to the front as the porch. However only five sides of the octagonal prism are
exposed. The main part of the house has been capped with a square pyramid.
The front elevation of the bungalow shows 3 arches which have sacred connotations in
both Western and Chinese societies. Arches have been around since the Roman era where
an arch would be erected to mark a victory of empire. The 3 arches also represent the
15
trinity in Christianity and the character 3 in Chinese is pronounced the same was as the
character for “life”. this is also the reason why tim sum pieces are always served in 3s.
Buildings with Octagonal Pavilions
Chinese Temple along Upp Serangoon Rd
Former factory at Neil Rd
The number 8 is the considered the most auspicious number by the Chinese as its
pronunciation sounds similar to the Chinese character for “prosperity”. Hence octagons
have also found among the Chinese because they resemble a ba kwa mirror, a octagonal
piece of wood inlayed with a mirror in the mirror. A ba kwa mirror is hung above the
entrance of a Chinese home to ward off evil. The use of octagonal pavilions in Chinese
owned premises as seem above is most appropriate.7
Why Tiger Balm Oil is sold in a bottle with an octagonal cap?
The factory at Neil Rd (right picture) once belonged to the Haw Par brothers who made
their fortune by selling their famous Tiger Balm Oil. As traditional businessmen who
wanted good business, they had a octagonal turret added to the roof of the factory to ward
of bad luck. This is the reason why Tiger Balm oil is still sold in a bottle with an
octagonal cap.
7
A. T. Mann , Sacred Architecture, (Dorset: Element Books) , 1993, pp. 77 - 85.
16
4.2
A Retreat to the Past?
Traditionally, local architects used to look to their counterparts in the West for inspiration.
However, in the past 15 years, there seems to be a revival of buildings that have been
inspired by Chinese tradition and beliefs.
Modern Octagon to Ward off Evil
Façade of office block simply called No 79 Anson Rd
Here on the façade of this office block, we see a repeated pattern based on the motif of an
ancient Chinese coin. The ba kwa motif is also displayed prominently above the row of
Chinese coins. Clearly the architect had the concepts of fung shui in mind when he
decided to put such a designs on the façade of the office block in the hope that these
auspicious symbols will indeed bring prosperity to the building’s occupants.
17
4.3
Tradition and Geometry:
UOB Plaza at Raffles Place
Close up of Tower I
Close up of Tower II
The UOB headquarters at Raffles Place consists of 2 office towers joined by a glass
atrium. The shorter tower (Tower I) was the original UOB office block that was built in
the mid 1980s and the taller tower (Tower II) was completed in 1993. The older tower
was renovated to the same style as the new tower.
The Chinese believe that a “ba kwa” mirror (an octagonal gilded mirror) is believed to
ward off bad luck and protect the inhabitants of a house when it is hung above the main
entrance. Here instead of a “ba kwa” mirror, Tower I of UOB Plaza is shaped like an
octagon prism but the rational behind the shape remains grounded on fung shui principles.
After the completion of Tower II in 1993, Tower I was made taller after a new “crown”
was placed on its top. On closer examination of Tower II, it is observed that the base of
Tower II is in effect a rectangular tower block with 3 “cubes” of decreasing sizes placed
one on top of another , with each “cube” turned at an angle. This gives rise to the
interesting star effect of the building. Lastly, this star effect has 8 points which also
takes Chinese numerology into account as the digit 8 also sounds like “to prosper” in
Chinese.
18
4.4
Islam’s Sacred Geometry
Hajjah Fatimah Mosque at Beach Rd8
The mosque was paid for buy funds donated by a wealthy Bugis businesswoman in 1846.
She had commissioned a French architect to build the mosque for her which explains why
the minaret resembles the steeple of a Christian church.
The spire, which is leaning slightly, consists of four levels. A square base rises out of the
boundary wall and is decorated with classical elements such as pilasters with Tuscan
capitals and an arched recess panel. This is surmounted by octagonal second and third
levels of diminishing size, and an elongated steeple like structure9.
Islam has a tradition of a symbolic and sacred geography which is an attempt to correlate
the spiritual world with mathematical dimension of the physical world through
geographic coordinates. The transition from rectangular to spherical geometries occupied
a primary position in the minds of the Islamic builders due to the paramount importance
of Mecca, and the requirement of daily worship in its direction, which meant that
sophisticated geographic science is required.10
8
All photos of the Hajjah Fatimah Mosque have been taken from the Online Photo Archives of the
National Heritage Board, http://picas.nhb.gov.sg
9
Liu, In Granite and Chuna,pp. 92 – 98.
10
Mann, Sacred Architecture, pp. 121- 127
19
The geometries in Islamic architecture are symbolic. The six squares faces of the cube are
earthy, the twenty equilateral triangles of the octahedron are airy, and the four equilateral
triangles of the dodecahedron are symbolic of the universe as a whole. These shapes can
be observed everywhere in the architecture.
The main prayer hall is surrounded on three sides by spacious verandahs. These are
enclosed with repetitive lancet-shaped arched openings framed by patterned screens.
Between each of the arched openings is a minaret: a column rising out of a pedestal base,
with an octagonal shaft and a miniature calling tower rising above roof level.
The dome has 12 lancet-shaped windows, three at each cardinal point, with yellow and
green stained glass. The sphere of the dome with its 16 ribbed divisions (representing the
4 main cardinal points and their sub-divisions) is the focal point of the interior.
20
5.
Art Deco and Geometry Galore
The Western world emerged totally different after the Great War (WWI). A new
social order had been forged and European architects began to reject classical architecture
which was linked to decadent monarchies which represented social inequality.
As a result, a new style popularized by German architect, Walter Gropius’s
Bauhaus, became fashionable. Bauhaus buildings have flat roofs, smooth façades, curved
balconies, horizontal windows and a white-washed cubist look. This modern movement
spawned the art-deco style which replaced old decorative practices with new geometric
patterns which classical details on an essentially classical façade were simplified.
Art Deco exemplified the zeitgeist of the 1920s which was filled with hope and
excitement. This new aesthetic movement was seen as the style of the future and social
advancement as it embraced the new machine age and made reference to modern ships
and airliners and fast travel.
5.1
What Makes up an Art-Deco Building?
From the 1920s to just before the outbreak of WWII, the Empire State Building
and the Chrysler Building found in New York inspired and fired up the imagination of
many architects who sought to recreate the decorative elements of these buildings into
their own creations.
Therefore, to list the main features of an Art-deco building, it is
necessary to first study the Empire State and Chrysler Buildings11.
i. Most Art-deco buildings have a flag pole in the middle of the building, sometimes
resting on a “star burst” effect (Chrysler Building).
ii. Decorative elements consisting of geometric shapes are often concentrated at the
top of the building.
11
Photos of these 2 buildings have been taken from www.greatbuildings.com
21
iii. The building gets narrower towards the top and is often crowned with a ziggurat
(square pyramid) (e.g. Empire State Building).
iv. Architects also got inspiration from ships which were the most common and
advanced means of travel after WWI.
Chrysler Building
5.2
Empire State Building
Examples in Singapore:
a) Highly stylized pyramids which have been pared down
Entrance to Chinese Temple at Beatty Lane
Shophouse at Tyrwhitt Rd
22
b) The flag pole and the “starburst” effect.
Clifford Pier at Shenton Way, opened in 1933
c) Building with balconies resembling the decks of ocean liners. Notice how the pole
remains.
Apartment block at Hamilton Rd
House along Upp East Coast Rd
23
5.3
Amalgamation of Prisms
Art-Deco bungalows along Bukit Timah Rd
This unique bungalow on the left is located along Bukit Timah Road, just off Sixth
Avenue. The focus of interest is undoubtedly in the use of a cylindrical tower which has
been attached to the end of the rectangular main block. Although the location of the
turret departs from the general trend of vertical symmetry that all buildings should have,
the building remains elegantly well proportioned.
As with both buildings, the clean linear lines of the building that are reminisce of a ocean
liner are brought about by the cantilevered edges of the building. These ledges also
emphasize the horizontal effect of the house which is in turn balanced out by the
placement of full-height windows on the façade.
24
Art-deco office building at Circular Rd (behind Boat Quay, circa late 1920s)
This is Singapore’s very own version of New York city’s Flatiron building (refer to
picture on the right). This is the only example of an Art-deco era building in Singapore
that has been built in the shape of a wedge (or a triangular prism). The shape of this
building was necessitated by the fact that like the New York Flatiron12, it is located at a
road junction.
When a person stands in the front of the building and looks up, the rectangles (formed by
the window frames) accentuate the height of the building and the horizontal cantilevered
ledges emphasize the horizontal effect of the building. Hence we see that even with
mere geometric shapes, it is possible to achieve a level of architectural sophistication that
can match complicated classical architectural styles of the past.
12
Picture taken from www.greatbuildings.com
25
Modern Interpretation of Art-Deco
The façade of the Singapore Institute of Management at Clementi Rd built in 1995 is
clearly art deco with generously proportioned rectangular turrets flanking the main
entrance. Here, it is interesting to observe how the entire façade has been ornamented by
manipulating the size of rectangles.
26
6.
A Call to Disorder and Giant Geometry
An Introduction to Post-Modernism
Postmodern architecture has its roots in the late 1960s after architects found that the
modern movement first started by the Bauhaus in the 1920s was beginning to get stale.
New ideas are combined with familiar forms to make statement or just serve as a visual
delight. Previously geometrical patterns or shapes were used as ornamentation on a
building, but now the building has become the geometric shape. The whole new range of
provocative buildings may surprise, startle or even amuse the beholder.
6.1
Where Shapes are the Structure
Wheelock Place at Orchard Road,
completed in 1996
Interior view of the glass cone
a
Wheelock Place is an excellent example of a postmodernist building as it has chosen to
break away from the conventional box shape. Here the façade is nothing more than a
27
huge glass cone. While geometric shapes have always played a role in decorating the
facades of buildings, this is the first time in local architecture that a cone actually is part
of the structure and houses the atrium of the office block.
The “greenhouse” which is the Fish & Co restaurant at Park Mall is also a case of
geometric shapes grouped together to form a structure. The rough components of the
building are cubes (as the main dining hall) and square pyramids (as the roof).
Singapore Telecoms Communication Tower at Buena Vista
The Singapore Telecoms Communication Tower is a building with an extremely
interesting design. It is in the shape of an inverted “L” that had gone through several
28
transformation. The overhanging parts of the building have gone through four fold
rotational symmetry and then translation is carried out to achieve the interesting effect
that the building has.
Modern Obelisk
Centennial Tower at Millennia Walk is made of a rectangular central shaft capped with
a square pyramid with the apex removed. In addition the “flattened pyramid” is supported
by 4 octagonal prisms which are encased with a highly reflective metal. Each of 4
octagons has 3 faces exposed and reflects the sunlight, making the tower sparkle in the
day. From afar, Centennial Tower resembles a modern obelisk and its unique shape
makes it stand out prominently from its neighbors.
29
“The Colonnade” at Grange Rd
Instead of the usual glass paneled façade, the “Colonnade” goes against convention and is
best described as a series of cubes stacked in a confused order. The projections and
recesses of the cubes are organized in such a way that each apartment has a balcony on
the roof of the apartment immediately below and also allows for maximum light to enter
into most areas of each apartment. It is very interesting to see how mere cubes can give
rise to such an interesting texture on the façade.
30
6.2
The Effects of the Works of Piet Mondrian
Examples of Paintings created by Mondrian13
Piet Mondrian ,
Born
Died
March 7 1872, Netherlands.
Feb 1 1944, New York, USA.
14
The subdivision of a rectangular space (of a building) has always been the primary
concern and challenge of any architect. The rectilinear lines of Mondrian’s paintings are
thick and often filled in with primary colours (red, yellow, blue). Although this results in
the painting being nonsymmetrical, it remains visually proportional and balanced to the
viewer. This is also something that architects wish to emulate. Therefore, Mondrian’s
paintings have been widely attributed to the development of post modernist buildings in
which one finds regularity on an irregular façade.
With the departure from classical architecture, function did not have to follow form, i.e.
buildings did not follow a standard boxed shape of old buildings that were discussed in
13
Pictures taken from the online store “All Posters.com” which specialise in reproductions of famous
paintings. http://www.allposters.com/gallery.asp?aid=85097&item=323522
14
Photo of Mondrian taken from “The Artist” website at
http://www.the-artists.org/ArtistView.cfm?id=8A01FA1A-BBCF-11D4-A93500D0B7069B40
31
the earlier chapters, but rather the layout and appearance of a building (the form) would
follow its use (function) as mooted by Louis Sullivan in the late 19th century.
No shape plays as important a role in architecture as the humble rectangle. It is the most
adaptable shape for Man’s constructive needs in geometry. Streets, land parcels,
buildings, rooms, doors, windows, furniture are usually rectangular. Unlike other shapes
such as the square or cone, there is no fixed proportion of rectangle which satisfies our
daily needs. The application of the rectangle as a building factor is governed by its
proportion and aesthetic purpose, i.e. the with to length ratio. Yet a balance can always
be achieved like the random rectangles on a Mondrian painting. 15
The Gallery Hotel at Robertson Quay: A modern interpretation of Piet Mondrian
16
The façade of the Gallery Hotel is a veritable explosion of coloured rectangles of
different proportions in both the horizontal and vertical planes exactly like a gigantic
Mondrian painting. The big windows enclose the suites of the hotel which require a
larger window for maxium illumaintion of the room in the day as well as a better view
15
16
William, Blackwell, Geometry in Architecture, (New York: John Wiley & Sons) , 1984, pp. 70 -75.
Photo taken from the official Gallery Hotel website at www.galleryhotel.com.sg
32
out of the room that would have otherwise been restricted by standard small windows.
Normal rooms of the hotel have been smaller square windows which are also
proportional to their size.
Orchard Cineleisure Multiplex at Orchard Rd
While the colour scheme has clearly been influenced by Mondrian, it is a shame that the
architect of this building did not continue to follow the other principles of having form
follow function as we can see that the colourful features only serve a decorative function.
8.
Geodesic Domes
33
Many cultures of the world have been fascinated with the dome as it is one of the
most sophisticated regular solids known to Man. The dome is the most compact of the
solids and is the structure with the highest ratio of enclosed area to external surface area,
and in which all structural members are equal contributors to the whole. While the
traditional dome that adorns churches and grand manors has remained largely similar in
design for the past 600 years, a major break through in the application of the usage of the
dome was made in the late 1940s by Richard Buckminster Fuller. Fuller had developed
the Geodesic Dome in the late 1940s as a possibly solution to solve the acute housing
problem in the post WWII years. A geodesic dome is a type of structure shaped like a
piece of a sphere or a ball. This structure is comprised of a complex network of triangles
that form a roughly spherical surface. The more complex the network of triangles, the
more closely the dome approximates the shape of a true sphere.17
Fuller had developed his Geodesic Dome by altering an icosahedron by
adding triangles to comprised of a complex network of triangles that form a roughly
spherical surface. The more complex the network of triangles, the more closely the dome
approximates the shape of a true sphere (please refer to diagram below18).
17
18
Blackwell, Geometry in Architecture, pp. 173 -182.
Diagram taken from website of John W Rich at http://homepages.ihug.co.nz/~jw.rich/about.htm
34
Real Life Application of Fuller’s Geodesic Dome
The unconventional shape of Fuller’s invention made it very difficult for the public to
accept it socially as a viable means of housing. The basic shape of the dome made the
placement of furniture quite problematic since most furniture pieces were either square or
rectangle and could never be put against the interior of a dome which was curved.
However, some uses did eventually arise for the geodesic dome because of their inherent
properties.
a) Geodesic domes can withstand hurricanes and earthquakes better than conventional
buildings.
Because of its spherical shape, the geodesic dome becomes more aerodynamic and
remains very stable even in strong wings up to 210mph. In fact, the geodesic dome is
commonly used as permanent dwellings for scientists who have set up their bases in
the artic circle.
b) The geodesic dome is the strongest, lightest, and most efficient means of enclosing
space yet devised by man19.
The frame of a geodesic dome is made up of steel joints and the structure of the dome
allows equal distribution of the total weight on all joints. This results in greater
stability of the entire structure. Scientist who wish to create a secure environment for
their experiments often use the geodesic dome as a biosphere.
19
William Lauritzen, Geodesic Dome Education: An Introduction,
http://www.earth360.com/math-dome-ed.html
35
c) Famous geodesic domes include Disney’s Epcot Centre in Florida.
Singapore’s very own Geodesic Dome … the Orchard MRT Station
Interior of the Dome
The dome has a huge span as it covers the entire hall of Orchard MRT station, however,
the entire structure is being held up without any beams or pillars. Narrow metal rods that
have been assembled like isosceles triangles have sufficient strength to support the dome,
giving the MRT station a very bright and airy feel to it.
36
Bibliography
Aslaksen, Helmer, “Mathematics in Art and Architecture”,
http://www.math.nus.edu.sg/aslaksen/teaching/maa/Symmetry_in_Art_and_Architecture.ppt
Blackwell, William, Geometry in Architecture, (New York: John Wiley & Sons) , 1984,
Ching, Frank, Architecture, Form, Space & Order, (New York : Van Nostrand Reinhold) ,
1996
Fullerton Hotel, The, www.fullertonhotel.com
Gallery Hotel, The, www.galleryhotel.com.sg
Great Buildings Online, http://www.greatbuildings.com
Lauritzen, William, Geodesic Dome Education: An Introduction,
http://www.earth360.com/math-dome-ed.html
National Heritage Board, Online Photo Archives, http://picas.nhb.gov.sg
Rich, John, Geodesic Domes, http://homepages.ihug.co.nz/~jw.rich/about.htm
Stevens, Gary, The Reasoning Architect: Mathematics and Science in Design, (New
York : McGraw-Hill), 1990
Please note that all photos found in this project have been painstaking taken by the group
members of this project unless stated otherwise.
37
38