The Design of Space based on Architectural Geometry

Wasilah

Department of Architectural Engineering, Faculty of Science and Technology, Universitas Islam Negeri Alauddin

Makassar, Indonesia

Keywords: Expressional space; geometry architecture; pure geometry; composition of geometry; mural art; skateboard;

space form.

Abstract: Aim of expressional space is to facilitate the public to explore their hobby and talent autodidactically. The

space for expression in Makassar City is necessary for mural artists and youngsters who have a hobby to play

skateboard. Their talent receives insufficient attention from the government, thus creating negative attitude

because there is no space to accommodate their activity. Therefore, this paper presents a design idea of

expressional space by implementing architectural geometry. The architectural geometry design principle is

based on simple geometry form application as a realization of form from the space. An experience of the

space for the user is realized by the relationship between the space and the interaction with the environment

through geometry and form processing as the basic of the creation process in the architectural works. Content

analysis method provides a landscape layout and transformation of form and building mass in form of the

implementation of architectural geometry principles. The principles are pure geometry, composition of

geometry, direction wall, and opening for the transformation process of expressional space form to produce

and increase aesthetic value of the environment.

1 INTRODUCTION

The definition of architecture, based on the book

of Hybrid Space, is “The art or science of building,

specifically, the art or practice of designing

structures, especially inhabitable ones”. This

definition sharply defines the architecture as an art.

An art definitely addresses something in aesthetic

value. Kimberly Elam expresses “Architecture has

some of the strongest educational ties to geometric

organization because of the necessity for order and

efficiency in construction, and the desire to create

aesthetically pleasing structures”. She explained that

the architecture has a strong relationship with

geometry. One of the connections between

architecture and geometry is aesthetic value.

Therefore, obviously more services in architecture,

such as building architectural service, landscape

architecture, the city architect, and etc., are popular

nowadays.

According to the definition, geometry is one of

elements to present an aesthetic value in architectural

works. In fact, in order to create aesthetic value, the

architecture work should follow the geometry

principles. This principle will define the result of the

architecture form. One of the examples in geometry

principles is the golden section.

A roman architect, Marcus Vitruvius, explained

that the developer must always practice the precise

ratio in the development of a temple, he stated “for

without symmetry and proportion, no temple can have

a regular plan”. Every existing temple at that time

must practice the golden section. As a result, the form

of most temples at that time were fairly similar and

standard. According to the limitation of the golden

section, there is a creative ideas limitation on the

architects and architecture diversity at that time.

“The purpose of geometry of design is not to

quantify aesthetics through geometry, but rather to

reveal visual relationships that have foundations in

the essential qualities of life, such as proportion and

growth patterns as well as mathematics. Its purpose

is to lend insight into the design process and to give

visual coherence to design through visual structure.

It is through this insight that the artist or designer

may find worth and value for themselves and their

own work”. Description from Kimberly Elam on the

Wasilah, .

The Design of Space based on Architectural Geometry.

DOI: 10.5220/0008908500002481

In Proceedings of the Built Environment, Science and Technology International Conference (BEST ICON 2018), pages 76-83

ISBN: 978-989-758-414-5

geometry function has explained that geometry has

relevant function to express the visual relationship of

an object based on its proportion and also the

development pattern of the object.

The geometry function is practiced on the

building architecture. If the painting and the building

have no geometry principles then the building is

considered to not have aesthetic value at that time.

However, there are a lot of paintings and forms

without geometry norm and those works may still be

categorized as an aesthetic works. Obviously, the

geometry rules in a design would limit the result of

design variation. Other than as visualization

relationship and a proportion of an object, geometry

has a function as a norm to present a size in a building

and shape.

Geometry is one of mathematics sciences that is

implemented in the architectural world and one of the

branches of science that is associated with size,

composition, and proportion. One chapter in the essay

of Dr. Joachil Langhein has stated that “Proportion

as a guiding pattern for establishing beauty.”

Moreover, the proportion has a close relationship

with geometry, even non-geometry procedure

possibly presents a proportion. The proportion in a

geometry is related to symmetry that controls axis

reflection, rotation, stretching, and etc. The geometry

presents because of proportion and building

symmetry. A geometry with symmetrical element

provides a beauty in a building. According to

Mangunwijaya definition, “Beauty is a matter of

subjective. A culture of humanity will define the

standard of a beauty based on their community

(Dayak and Buginese ethnic group probably will have

a different understanding in the definition of

beauty)”. Their definition of beauty will be passed

down through generations and create a specific

'beauty' mindset. Architectural aesthetic of traditional

building is one of the origins of the culture.

Mangunwijaya has interpreted that a beauty is

from a cultural, traditional building. Additionally,

more definitions of freedom of expression in the

context of geometry are: Every people who follows

design processing will present a different product,

even if they have an equal trigger. A diversity that

exists in respective products is one of illustrative

examples in term of 'freedom of expression'. This

freedom refers to an understanding where geometry

does not limit freedom of expression in architecture.

This definition draws a conclusion which stated that

geometry principle in a design could restrict the result

of a design variation. This understanding has changed

along with the exploration of form, function, and

various expressions of architecture with the

application of geometry.

Finally, we will return to the basic of architecture.

Mangunwijaya, in the book of Wastu Citra, has

written: "Berarsitektur or how to make an

architecture is a language in terms of space and

aspect or gatra, along with line, plane, material, and

ambiance. We should create a proper architecture

according to the culture, accompanying the feelings

and responsibility in the application of a proper

architectural language." A beauty in architecture is

architecture that is aware of the value-in-use,

following the aesthetic value as spiritual level inside

the design. The result is not only a product that is

placed as "a statue", but the result is also something

that should provide an investigation on a meaning or

three dimensions (or even four dimensions).

Geometry never limits the expression in an aesthetic.

In fact, geometry offers a freedom in the language of

space, line, and plane.

Briefly, geometry will present a beauty in

architectural art, either in form of place or ornament

and symbol. Geometry can represent an expression in

a space. A difference in respective space function is

frequently explained with a different expression. In

other words, the function will produce an

expressional form. Generally, the expressional space

is an accessible public area for all society. The public

area is part of an environment completed by a pattern

and function as a socialization and communication

area in the society. Principally, the public area will be

defined as a place to facilitate specific activity or

interest for the people either individually or in the

community.

The existences of expressional space have an

influence on the economic development and social

conflict that occur between young people because the

expressional space becomes a facility to express their

interest and individual skill. Examples of hobby

activities are skateboarding and mural painting.

Skateboarding and mural painting are activities that

heavily consume more physical and mental energy.

These activities become popular activities in

metropolitan cities in Indonesia, including Makassar.

Based on this phenomenon, an idea was hit upon

to create an open space to facilitate skateboarding and

mural community in Makassar to limit the problems

of street dysfunction and vandalism of public

facilities on some streets in Makassar. The design of

the public area is expected to become a space for

skateboarding community to express their hobby.

Additionally, mural community will have benefit too.

They can exhibit and sell their artworks. Moreover,

the result may bring an increase in creative economy

The Design of Space based on Architectural Geometry

sector for youngsters in Makassar. Furthermore, the

aim of the design will welcome the existences of

skateboarding and mural community in Makassar and

these communities can socialize with the society. As

an open space to facilitate sport and art community,

then the inspiration of space concept is architectural

geometry concept that emphasizes the space aesthetic

art.

The other side of geometry is the order in

geometry creation. People tend to produce a set of

rules in their lives. Architecture is a facility to meet

the needs of life and to require the application of an

order. The form creation cannot be separated from the

regular forms. The geometric shapes appear to

reinforce the impression of space and to create an

interior in geometry.

2 METHODS

The research method is site observation data about

a potential condition and land suitability for arts and

sports area. Then, the data are processed by content

analysis method. Content analysis approach

conducted in this study will realize the result of the

design with architectural geometry application.

Fundamental concept in 'image' design of

expressional space for mural art and skateboarding

refers to object-oriented geometry form. Therefore,

the design concept may be categorized into

architectural geometry approach method, specifically

pure geometry; the composition of geometry;

direction wall; and opening. During the design

process, the fundamental concept is combined with

the planning of geometry calculation with symmetry

principle. Architectural geometry principle

emphasizes building aesthetic and high-quality of the

environment. As a result, the design creates a building

mass forms, correlates environment potency, and

solves the landscape problem.

The analysis in design approach is to identify the

architecture component of geometry, including:

a) Geometry principles include an explicit

composition of geometry form which is the

pure geometry forms: square, rectangle,

circle, and triangle.

b) The composition of geometry. A shape of

geometry is not absolute. Therefore, the form

is part of the transformation process, a form

transformation may be understood as a result

of variance from existing basic form

manipulation.

c) Direction wall consists of wall to cover a

space and building. Sometimes the wall may

refer to a building envelope. The wall is one

of important elements to present a form of a

building. The wall visual is dominant rather

than the element of floor and roof plane as

part of the building envelope.

d) The opening. There is a close relationship

between the opening and the wall. The visual

space quality is certainly determined by the

opening. For example, the wall opening

organization will produce a reflection of

illuminance. Generally, the opening will

frame and receive the landscape view

enjoyment from the interior area, as part of

indoor and outdoor confrontation. The

opening may be identified as a large opening.

The large opening is a result of size reduction

of form, or vertical opening, of the building

mass volume. It is also an opening from the

interval between every wall surface.

Early design concept determines transformation

theme definition that will be applied in the building

design. Figure 5 describes the correlation between

definition and application of building theme.

a) Appearance

Appearance definition approach of the

building will exist in the building facade. The

form completed by presenting the theme is

geometry form, which describes a beauty in

architectural art, either in form of place or

ornament and symbol, and contains the concept

of balance, rhythm, vocal point, scale, and

building integration.

b) Well-Defined

The building should have a well-defined

space organization. Design finishing process is

area division which is according to space

function, commercial area, and facility area;

organization of space division area is based on

characteristic and space feature.

c) Opening

Approach of the open definition in the

building will be manifested in building interior,

space organization, and building facade.

Open/transparent design of most interiors apply

natural air ventilation and glass material for

natural lighting in interior shading art.

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3 RESULTS

3.1 Landscape Layout Transformation

Based on Architectural Geometry

Principles

The landscape layout transformation is needed to get

a good view

3.1.1 Pure Geometry

The site pattern was created from the combination

of pure geometry shapes, such as square, rectangle,

circle, and triangle. Each pure geometry shape will be

synchronized with the function of the facilitated

activity. The square shape represents the supporting

facility area and mural area. The rectangle shape

represents skateboarding area, field, Bosowa sport

centre, and management office. The circle represents

a rounded green area and fountain spot. The triangle

represents the triangular park area, parking area, and

mural area. The shape of pure geometry was

organized carefully to create and improve the

aesthetic value of the site plan. The combination

result of pure geometry shapes, such as square

rectangle, circle, and triangle, is described in Figure

Figure 1. Combination of pure geometry shapes,

square, rectangle, circle, and triangle is a basic of site

plan layout pattern formation for expressional space.

Figure 2. Allocation of space function based on

activity types in the area.

Figure 3. Realization of expressional space with the

application of pure geometry shapes element.

3.1.2 Geometry composition

As described in Figure 1 and Figure 2, there is a

form transformation which is a result variances of

existing basic shapes manipulation, such as the

combination of rectangle and triangle shape and the

combination of square and triangle shape. The

processes of basic form manipulation can be seen on

figure 4 below:

-Composition 1:

-Composition 2:

-Composition 3:

Figure 4. The processes of basic form manipulation.

There is a complex form composition in the site

plan design of the front of mural area entrance. The

composition shapes are square, triangle, circle, and

rectangle that create a pure geometry form. In

The Design of Space based on Architectural Geometry

addition, there is a separate part of pure geometry

form, but the form has been transformed.

Figure 5. Mural area perspective

3.2 Transformation of Form and

Building Mass Based on The

Architectural Geometry Principles

3.2.1 Pure Geometry

There are mass buildings in the site plan design, a

sport center, and skateboarding area. These areas are

supported with infrastructures, such as management

office, cafeteria, musalla, and other infrastructures.

The building shape consists of rectangle and circle as

the basic form, based on the skateboard form which

is distorted into the main building form idea in the site

plan design. Additionally, the main building facade

has implemented geometry pattern to strengthen the

geometry concept as a design approach concentration.

Geometry pattern in the facades consists of a circle,

triangle, and square as the basic forms.

Figure 6. The skateboard basic form consists of

rectangle and circle forms.

3.2.2 Geometry composition

The building formation is similar to a rigid box of

rectangle completed with a massive wall that covers

the entire building. The rectangle and circle, which

are pure geometry forms, gradually has transformed

and categorized as a simple transformation form. The

form is a result of metaphor process from a

skateboard form. Moreover, the final result of the

building design adapted the traditional house of

Makassar Bugis ethnic group. According to the

structure, the vertical building consists of foot, body,

and head. As a result, the vertical main building

consists of three main parts, similar to Buginese

traditional house structure, which also has three

structures (foot, body, and head).

Figure 7. Transformation of building form

Figure 8. Main building ground plan on the second

floor. Colour: Red (rectangle shape), Blue (square

shape), Yellow (composition 3), Grey (building

corridor).

Figure 9. Main building ground plan in the third

floor. Colour: Red (rectangle shape), Blue (square

shape), Yellow (composition 3), Grey (building

corridor).

According to the building ground plan, the square

and rectangle structure is an intersection. The free-

standing wall of the building is the intersection from

one space to another space to create the interlocking

entrance area. The free-standing wall positioning with

similar pattern creates an interior room with an

opening in the wall as illuminance area receiver. The

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geometry composition is a simple transformation

form but the composition creates a visual interaction

inside and outside the building.

3.2.3 Direction wall

Basically, the function of the wall is as the cover

of a space and building, and the part of building

envelope. According to Tadao Ando, walls are the

most basic elements of architecture. Wall is a border

between the interior and exterior, but at the same

time, wall can also be the most enriching element that

will transform the form of a place and create a new

form or new space.

Wall is an important element to present a form of

a building because the wall is visually more dominant

rather than the ground plane and the roof plane, which

are also the building envelope element. The floor is

not directly visualized because the floor area is

hidden by the wall and the roof plane is usually a flat

cover plane. The sport centre main building with

dynamic wall positioning creates and divides the

space. The wall function is as a direction wall of a

movement or user circulation line in the building,

although the circulation track impression is in form of

straight line and fairly simpler than the building

entrance towards to other rooms inside the building.

The exterior wall of sport centre building includes

and covers most part of the site. The building contains

glass material to support the visitor with two

atmospheres simultaneously, the indoor with modern

vintage ambiance and a fascinating outdoor view (a

collaboration between mural art and the park). The

glass material is from geometry pattern with triangle

and square form combination.

Figure 10. Geometry pattern in the exterior wall

3.2.4 Opening

The opening and wall in the main building design

of sport centre are two closely interrelated parts

because the quality of visualization room is exactly

determined by the opening. The opening becomes the

part that organizes the wall panel to create

illumination possibility in natural ways. Most of the

openings are to frame and receive the landscape view

in order to enjoy it from the interior room and also as

an indoor and outdoor confrontation. Indoor

expressional space is an opening in form of a vertical

and large opening in building mass volume and an

opening from the interval of the wall surface.

The third floor has an opening in the wall panel

continuously to provide a natural illumination inside

the building and to improve the quality of space.

These openings are located on every side of the

building. This is one of the efforts to gain a benefit of

landscape condition around the building as

supporting aesthetic element from inside the building.

In addition, the second floor has a touch of glass

material opening to include the illumination element

as a lighting in the transition area from inside to the

outside, or vertical opening. The second-floor

opening will frame and present a vista, such as park

and mural art display, as a technique to combine the

inside and outside of the vertical opening. A

patterned-glass material creates a reflection with

geometry forms.

Figure 11. Opening in the main building. Number: 1

(Opening on the third floor), 2 (Opening of the

second-floor building with a patterned-glass

material)

4 DISCUSSION

The site pattern design practiced the basic

principles of geometric architecture. The

implementation is gradually from the shape of pure

The Design of Space based on Architectural Geometry

geometry covering triangle, square, rectangle, and

circle. The basic form was transformed into a new

pattern and the transformation process is categorized

as a simple transformation form.

Basically, the site plan area has three functional

area categories, skateboarding attraction area, mural

area, and infrastructure for skateboarding and mural

areas. Skateboarding attraction area is indicated by a

blue color in Figure 2 and located on two different

areas, which are on both sides of the main building of

Bosowa sport centre. The mural works exhibition

display is located in the main street of site plan area.

A decision of skateboarding attraction area location is

based on the accessibility reason, creating an

accessibility for the visitor. Consequently, the

skateboarding area is located in the parking area as

the strategic area. Meanwhile, the mural area is

located in two different areas which are along the site

border in form of a high wall. The wall functioned as

mural media and another area is located right in the

entry point of the site. As a result, the visitor who

enters the site will directly experience mural art

atmosphere emphasizing the architectural geometry

principles in expressing an aesthetic value.

In the main building, geometric shape is visible on

the building's facade with a patterned-glass material.

The pattern comes from triangular and square shapes

with color degradation that aims to produce shadow

geometric pattern which is dynamic with the

movement of the sun. Meanwhile, the covering wall

of space in the building is simple with a grid pattern

formed from the arrangement of a square and

rectangular shapes to maximize the use of space for

various activities.

The design should create a balance between

complex form composition of art mural display and

simple spatial layout patterns. Although the geometry

form is applied quite simply, but the application of

architectural geometry principle emphasizes building

aesthetic and high-quality of the environment.

5 CONCLUSIONS

Geometry form will generate an aesthetic

architecture art, either in form of space or ornament.

Geometry can represent an expression in a space.

Geometry will produce an expressive form. The

geometry design principles -in form of pure

geometry, a composition of geometry, direction wall

and opening- are a representative form that is

explained in expressional space design. The design

idea is an architecture works that combine basic form

variations: square, circle, rectangle, and triangle.

These forms are carefully organized to create and

improve the aesthetic value of the area. The

presentation of geometry form is fairly simple but has

a variation. As a result, the creation of circulation

pathway is simple. The circulation track is created by

the direction wall. The application of simple

geometry form is an effort to maximize the space as

an area for skateboarding activity inside the building.

Moreover, most of the opening building parts are

vertical opening with a standard of user eye level.

Patterned-glass material opening produces a

harmonic geometric shadow formation.

ACKNOWLEDGEMENTS

Geometry will always exist in architecture in a variety

of building angles. Either the application of the floor

plan or the building facade, in two dimensional or

three dimensional, is not separated from the

geometric shape, judging from the elements of the

whole. The shape of this form may affect design in

the architectural concept. The other side of geometry

is the order of the creation. Humans tend to produce

a set of rules in their lives. Architecture that is a

facility to meet the needs of life is also required to

apply for an order. Therefore, the forms creation

cannot be separated from the regular forms.

Authors would like to show gratitude to the

Architectural Engineering laboratory staff, Faculty of

Science and Technology Alauddin Islamic State

University, for sharing their pearls of wisdom with us

during the course of this research.

REFERENCES

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Nobuyuki Endo.

Ekomadyo, A. S. 2006. Prospek Penerapan Metode

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Arsitektur [Prospect in Implementation of Content

Analysis Method in Research on Architectural Media].

Jurnal Ilmu Pengetahuan Teknologi dan Seni, Volume

10 (2), 51-57.

Elam, Kimberly. 2001. Geometry of design: Studies in

Proportion ang composition. New York: Princeton

Architectural Press.

Gill, S. S. 2010. A Study of The Characteristics of Natural

light in Selected Buildings Designed by Le Corbusier,

Louis I. Kahn and Tadao Ando (Doctoral dissertation,

Texas A & M University).

BEST ICON 2018 - Built Environment, Science and Technology International Conference 2018

Hassan, Soraya Masthura. 2017. Prinsip Desain Geometri

Arsitektur [Design Principles in Architectural

Geometry], Tadao Ando. EMARA Indonesian Journal

of Architecture, Volume 3 Nomor 2.

Mangunwijaya, Y.B. 2009. Wastu Citra. Jakarta: PT.

Gramedia Pustaka Utama.

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APPENDIX

In this appendix, we present the collected data about

dimensions of the built space used for optimization of

spatial distribution based on the activity proportion.

Table 1. The size of build space

No Space Name Size (m

)

1 Ground Floor (Parking and

Service Area)

466.57

2 1st Floor (Skateboard Arena

and Management Office)

570.05

3 2nd floor (Cafeteria and

Musalla)

434.33

4 Security Room 33.8

6 Site plan 3811.08

Total of built space 5315.83

Based on the data obtained, the number of space

utilization planning area are:

‐ Built space of 5315.83 m²

‐ Planning footprint area of 39122.51 m2

‐ Percentage of constructed land is: 5315.83 m²

/ 39122.51 m2 x 100 = 13.587 m² or 14%

‐ Open space of 33.806 m²

‐ Percentage of open space : 33.806 m² /

39122.51m² x 100 = 86.410 m² or 86%

The percentage of master plan of expressional space

for skateboarding and mural communities in

Makassar city is 86% as the main functional area, and

14% as supporting facilities within the planning area.

The Design of Space based on Architectural Geometry