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The Role of Geometry and Proportions in Shaping the Fabric of
Space in Traditional Iranian Architecture: Case Study of
Mosques in Safavie Period in Isfahan
Mohamad reza mabhoot1, Seyyed Mahdi Madahi*2, seyyed ehsan sayadi 3
1,3
2
Faculty member, Khavaran Institute of higher education, Iran, mashhad
Ph.d student, Iran university of Science and Technology, Iran, Tehran and Faculty member,
Khavaran Institute of higher education, Iran, mashhad
ABSTRACT
Iranian architecture is found not in form, but in perceiving and creating space.
The main feature of traditional Iranian architecture can be defined as the
production of a space for living. In other words, architecture is first formed in
the mind of the architect and is then expressed and is finally placed on the
ground. Geometry has been the primary tool of all Iranian traditional architects
in creating architectural works. Considering that one of the most important
factors of creating a particular feeling in a space is its geometry, in the
architecture of buildings such as mosques, particular attention should be paid to
geometry and spatial proportions; this will not be possible unless we consider
the geometrical relations applied in traditional valuable mosques. As to the
creation of valuable buildings such as mosques, etc., Safavid architecture has
admirable features, and the culmination of architecture of this period is
observed in Isfahan. Therefore, the geometrical analysis of Safavid mosques
will reveal that how the architect's abstract ideas are converted into a plan. The
present research attempts to answer the following question: what factors have
affected the shaping of architect's abstract ideas of building the Safavid
mosques of Isfahan?
Findings of the study show that the art of geometry is a key element for making
connections between the building and the ideas that the builder has had in his
mind. This is not the material that creates his space; rather, it is his space that
requires a special fabric, and this is the point that our past architects have fully
understood. Methodology of this research is analytic-descriptive and it has been
conducted through geometrical analysis of Safavid mosques of Isfahan (Imam
Mosque, Sheikh Lotfollah Mosque and Agha Noor Mosque).
KEY WORDS: geometry and proportions, traditional Iranian architecture,
mosques of Safavid period, Isfahan
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Research questions
1. What factors have affected the shaping of architect's abstract ideas of
building the Safavid mosques of Isfahan?
2. How geometry has influenced the forming of mosques’ fabric of space in
Safavid period in Isfahan?
Introduction
Spatial forms of Iranian architecture can provide the experience of intimate,
personal and private environments along with huge and magnificent spaces.
They can provide the experience of closed, semi-closed, semi-opened and
opened spaces in combination with each other so that one feels that he has
found a shelter or has made an initiation. Basically, Iranian architect’s thought
for building a space is completely different from today’s methods. The Iranian
architect knew all that would change the insipid, rigid and neutral quality of
space. He was at the same time the architect, accountant, expert in materials,
and craftsman. He was so entangled with his contemporary society that he did
not need to separately study the required functions and later make their
diagrams, turn them into a map and finally have spatial imagination. He had
spatial imagination for the plan that he received from his employer. The
fundamental element and the basic theme of art and architecture are geometry
and proportions. It is in the systematic area of geometry and proportions that
everything including the components of a house and even a city can come into
existence. Creation of the nature, the entire universe including skies, earth, etc.,
and particularly the mankind has been based on geometry and proportions. In
Sura Al-Furqan, Verse 2, it has been stated that meaning that “It is He who
created all things and ordered them in due proportions” . If any of the works
which are created in this world are out of the essential measurements of the
nature, it will be unusual, unpleasant and unacceptable, and it cannot find a way
to the ideal state. In contemporary times, despite its evolutions and diversity,
lifestyle has been reduced to a number of functions, space organizing, and
forms. Contemporary architecture should revive all the lost areas of
architecture. Architecture is the creator of an environment in which life, with all
its aspects, is flourished and not suppressed.
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Literature review
By reviewing the background of the previous studies, it is observed that much
research has been conducted on the methods of using geometry as an efficient
tool in architectural techniques. We will take a look at some cases.
In an article entitled as The Sacred Geometry in Nature and Iranian
Architecture, Hejazi has geometrically analyzed a number of Iranian historical
monuments in which the golden ratio has been used and this has been the basis
of Iranian architecture aesthetics. Traditional architecture represents the cosmos
in earthly dimensions. In an architectural monument, all dimensions, both in its
integrity (height, length and width) and its components (including geometrical
surface patterns), are interrelated and never divorced from geometry (Hejazi,
2008).
In an paper entitled as Applying the Hanjar Triangles in the Mathematical
Calculation and Implementation of Geometry in Construction and Enforcement
of Traditional Iranian Architecture, Mahdizadeh Seraj, Tehrani, and Valibeig
studied the position of geometry in view of the architects and artists, and
demonstrated that past architects with their familiarity with geometry and their
ability in actualizing the geometrical relations, attempted to match the methods
of theoretical geometry with their own tools (Mahdizadeh Seraj, Tehrani and
Valibeig, 2011).
In another article entitled as Geometrical Analysis of Architecture of Sheik
Lotfollah Mosque to Find the Geometrical Relations between its Prayer Hall
and the Entrance, Dahar and Alipour have revealed some of the geometrical
relations between the components of this valuable building; and the position of
the prayer hall with the entrance has been determined by geometrical-graphical
methods. In designing Sheikh Lotfollah Mosque, golden ratio and its
construction geometrical methods have been used in making fitness between the
building components. As a result, the architect of this building, with his
comprehensive knowledge of geometry and the scientific methods of its
application, has skillfully adjusted the size and position of the building
components to each other and has made an eye-catching harmony between them
(Dahar, Alipour, 2013).
In this research, it has been attempted to have a geometrical analysis on the
architecture of Imam, Sheikh Lotfollah and Agha Noor Mosques in Isfahan, and
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thereby reveal that how the architect’s abstract ideas have been turned into an
architectural plan.
Methodology
Methodology of this research is analytic-descriptive and it has been conducted
based on library studies, documents, photos, as well as the geometrical analysis
of Safavid mosques of Isfahan (Imam, Sheikh Lotfollah and Agha Noor
Mosques). First these mosques are introduced, then they are geometrically
analyzed, and finally the results of the analyses are compared.
1. Geometry in architecture
1.1. Geometry is the disciplinary element of architecture, and organizes other
elements. In fact, geometry for architecture is the same as the thread for
beads, without which there is no organization and system for connecting
the beads to each other. Geometry provides harmony and continuity in
architectural works. As previously stated, in Iranian architecture,
geometry plays an important role. In fact, it can be considered as the
architectural language of Iran (Okhovvat, Baghayi and Bemanian, 2011).
1.2. Geometry is the main theme of all architects in creating architectural
works. What makes the works semantically different is the type and the
way of referring to these general components of architecture. In his
ascent, a Muslim architect creates the ever-best by the use of geometry
(Nadimi, 2000) (Diag.1).
Diagram1: source: authors
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In order to visualize a transcendental, provocative, sublime and timeless space,
the architect uses some unique principles and criteria in the building's structure.
Paying attention to order and continuously observing the proportions will lead
the architect to a pure, special and precise geometry (Bavandian, 2005).
2. The sacred geometry in Iranian architecture
The traditional architect uses geometry for having more exploration into the
natural phenomena so that he can lead the mind of the revelation-seeker from
the tangible world to the intelligible world. Geometry plays an essential role in
designing the Iranian architectural buildings. In terms of external function,
utilization of geometry as an art for creating forms, patterns and proportions,
reminds us of the world's Greatest Architect. Therefore, the art of geometry is a
key element in connecting the building to the builder's abstract ideas (Diag.2).
Diagram2: source: authors
Iranian architecture is a mirror which reflects the divine beauty – the one that is
sacred, and as a harmonic continuity of logical proportions, it can be reflected
through patterns that are exactly built based on the right proportions. The sacred
geometry is a powerful tool for creating the right proportions in architecture for
the sake of adapting the sky and the earth. The sacred geometry and the
proportions that are found in many forms of life in the nature are skillfully
applied by the traditional Iranian architect so that he creates a traditional
architectural object which is indicative of the right designing methods and the
correct engineering. Iranian architecture is the sacred geometricizing of the
divine beauty (Hejazi, 2009) (Diag.3).
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Architecture is first formed in the architect's mind (truth); it is then expressed
(medium); and it is finally placed on the ground or in the space (trope) (Diag.4).
Any type of architectural design is basically a work of geometry. Both deal with
the properties of lines, surfaces and forms in the space. Therefore, any analysis
on an architectural work is to some extent a research about its geometry. For a
mosque, the primary requirement is to provide a suitable space for the rows of
prayer-sayers who stand facing the Qibla, and based on a special manner, stand
on foot and then prostrate on the ground. Since circular or centralized designs
do not match this requirement, rectangular designs are more suitable for
mosques (Muhammad Al-As’ad).
The architect of a building like mosque intends to present a spiritual setting. To
do so, it is necessary that he reflects in the space the concept of divinity,
monotheism, and the soar of soul, so that his space creates the sense of
spirituality in the mosque. This is not the materials that create his space; rather,
it is his space that requires a special fabric and material, and this is the point that
our past architects have fully understood. Transparency whose roots can be
found in Iranian architecture at the time of the building of Takht-e Jamshid,
results from the very attitude of Iranian architects towards space (Haeri, 2009)
(Diag.5).
Diagram3: source: authors
Diagram5: source: authors
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Diagram6: source: authors
When creating a work, the artist creates a “jug” so that he leads the addressee
from “the visible jug” to “the invisible wine” through it, and conducts him from
what is visible to what is hidden from the addressee. He searches the scenes and
creates them, and then, through different means such as invitations, guidance,
movements, outlooks, emphases, combinations, etc., faces the addressee with a
condition in which he can feel that “sense” (Navayi and Haji Ghasemi, 2011)
(Diag.6).
Islamic historians such as Beihaghi, Ibn Khaldun and Khaje Rashid Al-Din have
written useful materials about architecture and architects. These people have
written that architects were familiar with mathematics and geometry, and when
they wanted to construct buildings, they attempted designing and mapping
before any other work. The great philosopher of Iran, Farabi, states that
architecture is based on the science of mechanics, and mechanics includes
skills, arts and techniques that are shown by skillful and artistic works in
geometrical forms (Kiani, 2012).
3. The role of geometry in mosques’ architecture
Considering the importance that it has in Islam religion, the architecture of
mosque as Muslims’ place of worship has always followed special fabric and
geometrical principles of its own period. One of the most important factors that
creates a particular sense in the space for users and consumers results from the
geometrical relations and proportions which have been applied in the
architecture of that space. Considering its application, any architectural building
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should have some properties that can meet the intended requirements of that
building. Using a suitable geometry which suits that function is one the
important tools of the architect for meeting a main part of the special
requirements of that building. In fact, the basic factor of creating unity among
the components of the universe, particularly among the components of the
corpus of each architecture culture, can be nothing but geometry. Although in
the history of architecture, in many of the buildings including personal houses
and even the rulers’ castles and palaces, and although today in some of the
buildings such as museums, offices, etc., the architect and the employer can
decide about the destiny of a building, in the architecture of buildings such as
the places of worship which have a special importance and position for people,
the architect cannot be inattentive towards the effect that his work has on the
addressee. Therefore, the task of building a mosque has been always assigned to
architects who were expert in mathematics and geometry and were so-called
engineers (Sattari Sarbangholi, 2012).
In the architecture of Iranian mosques, geometrical tools have been used
proportional to the temporal and spatial conditions and requirements of each
building (Dahar, 2013).
Safavid architecture, not only as to the creation of valuable architectural
buildings such as mosques, bridges, inns, etc. has admirable and special
features, but also the implementation of these works is indicative of an efficient
management in this period. The culmination of architecture of this period is
observed in Isfahan (Haji Kazemi, 2007).
Architectural features of this period are as follows:
The simplification of designs which, in buildings and spaces, are mostly
square or rectangle
-
Applying simple geometry and fragmental forms and lines
Modularization and use of equal parts and sizes in the building (Pirnia,
2011).
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4. Imam Mosque in Isfahan
The building process of the mosque has started in 1020 lunar year, and its
architect is Ali Akbar Esfahani (ibid).
Shaping traditions, ideals, slogans and religious concepts, the map that has
slowly progressed from the combination of the older and simpler types, huge
constructional elements and ornaments, all have been realized in the Imam
Mosque and that has ranked it among the biggest buildings of the world. The
forecourt which is almost constructional, has a sense of invitation which calls
the outside crowd to the shelter, security and refection inside the mosque. The
forecourt faces towards the North as it necessitates, but since sanctuary should
be faced towards Qibla (i.e. east north to west south), in order to prevent
deformation, much style and precision was needed; this problem was
successfully solved. People enter an excellent corridor through the forecourt,
which is one of the features of Iranian historical monuments in the past. This
corridor is circular and hence it has no direction; it can be like a pivot on which
the building’s axis rotates. The corridor opens into the tall arch of the northern
porch, and from its deep darkness one can suddenly observe the sunlit yard. On
the other side of the yard, there is the vast entrance of the seraglio which is a
window to another world of grandeur and centralized power (Pope, 2011).
4.1. Geometrical analysis of Imam Mosque
The ABCD square shows the northern porch of the mosque in which a circle
with center O and a radius half of the side of the mentioned square is drawn in a
surrounded way. We mark the point O” in the middle of the side BC and move
the drawn circle along the radius OO” so that its center is adjusted to the point
O”. With a 45o angle to the length of the horizontal line OO”, the radius of the
circle is drawn so that it crosses its perimeter in point S. If we extend the radius
O”S, it will be adjusted to the symmetry axis of the building entrance. With a
45o angle to the horizontal line OO”, the ABCD square turns and is placed
surrounding the circle O”. This square is moved to the center O”; A”B”C”D”.
From the middle of the side D”C” i.e. point N, an arch with radius NB” and
center N is drawn so that it crosses length D”C” at point E. The A”FD”E
rectangle that is obtained through this method is a golden rectangle1.
As explained, we extend the radius O”S so that it crosses the side FE at point Y.
The length O”S is adjusted to the symmetry axis of the mosque entrance and
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point Y is placed in the middle of the side FE. With the center Y of the point in
the middle of the side FE and with a radius equal to YM (M in the middle of the
side A”B”) an arch is drawn so that it crosses the length FE at point G. Once
again this is repeated for the other side of the entrance axis as follows: with the
center Y of the point in the middle of the side FE and with a radius equal to YN
(N in the middle of the side D”C”) an arch is drawn so that it crosses the length
FE at point H. In this way, the location of the two vestibules on the two sides of
the entrance axis is specified. The two rectangles ENIG and FMJH are golden
rectangles. After passing the entrance corridor, we arrive at the yard court and
can see the southern porch (Table.1).
Table1: geometrical analysis of Imam Mosque in Isfahan. Source: authors
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5. Sheikh Lotfollah Mosque
The smaller Sheikh Lotfollah Mosque (1012-1028 lunar year) is another
building of that period which is more easily perceived due to its fit size and
simplified function. Its firm domical form on a square-shaped room which is the
inheritance of Sassanid architecture has once again emerged in this beautiful
small mosque. This is an individual and interesting room which is more like a
private prayer hall. Similar to Imam Mosque, here for placing the seraglio
towards the Qibla, some adjustments have been made which require a 45o angle
from the northern-southern axis of the field. To do so, a creative and hidden
twist has been used in the corridor. When one enters the seraglio, sanctuary is
exactly in front of him (Pope, 2011). Passing the entrance door, we enter the
vestibule which is the beginning of a 28-meter corridor to the seraglio. Some
steps after entering the corridor, there is a grille on the right which provides a
view for the observer of the seraglio and it somehow encourages the observer to
continue his way. After that and in the middle of the corridor and before
arriving at the nick, there is a door on the left which leads to the winter seraglio.
14 meters after the entrance door, the corridor turns right with a 90o angle. At
the nick, there is a granite 100×70 cm window. Construction of such a corridor
with these ornaments and lighting, makes us think that this corridor has been
built not only for solving the problem of Qibla, but also for gradually separating
the worshiper from the outside commotion and for gradually preparing him to
enter another space. On the other hand, this corridor makes the eyes get used to
dim light. If the observer enters suddenly from the outside bright environment
into the half-bright seraglio, he cannot experience the grandeur of this space. In
order to show the light to the observer, the builder has first confirmed the lack
of light and then in the seraglio, he conducts the observer to the world of light
and color. After passing this dim corridor, we surprisingly enter the seraglio – a
world of color, pattern and light. And it is perhaps here and at this moment that
we find out the philosophy of building this corridor.
5.1. Geometrical analysis of the prayer hall space
First a circle with center O and a radius equal to the radius of the dome base is
drawn, which due to the squareness of the prayer hall, the mentioned circle is
surrounded by the square. With a 45o angle to the horizontal line, the circle
radius OA is drawn. The plotted circle moves along the radius OA so that its
center adapts to point A. Using this circle, the ABCD square with a side equal
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to the radius of the circle is drawn. According to the Table, it is clear that point
B is placed with very good approximation on the symmetry axis of the building
entrance and in the middle of the entrance doorway. With center K of the
middle point of the side DC and with the radius KB, an arch is drawn so that it
crosses the length DC at point F. The AEFD rectangle that has been so obtained
is a golden rectangle. At the final stage, the EGHF square is drawn. According
to the previous stages, it is clear that the length of the side of this square is equal
to the radius of the circle with center O. The BGHC rectangle is a rectangle with
golden proportion between its sides (Table.2).
Table2: geometrical analysis of Sheikh Lotfollah Mosque in Isfahan. Source:
authors
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6. Agha Noor Mosque in Isfahan
In Dardasht district of Isfahan, there is a mosque which has been designed based
on Iranian architecture traditions in the form of four porches. The entrances of
Agha Noor Mosque are located at the northern and eastern sides of the mosque,
which lead through the surrounding allies to Dardasht market and a same-called
district. The founder of the mosque, Noor Al-Din Mohammad Esfahani, was
one of the benefactors of his own time. Agha Noor Mosque’s seraglio is among
the most beautiful seraglios of Isfahan mosques. Its pillars are made from stone
and its numerous arches have some pieces made from transparent marble which
provides light during the day for the seraglio (Wikipedia website).
6.1. Geometrical analysis of the mosque
The usage of golden proportions can be observed in different parts of the
mosque. In the dome-house space, a circle with the center O and a radius equal
to the radius of the dome base is drawn, which due to the squareness of the
space of the mosque, it is surrounded by GHIJ square. With the center K of the
point in the middle of the side IJ and with the radius KH, an arch is drawn so
that it crosses the length IJ at point N. The GMNI rectangle which has been so
obtained is a rectangle with golden proportions between its sides. In the
springhouse next to the entrance corridor of the mosque, the ABCD square is
drawn. With the center X of the point in the middle of the side DC and with
radius XB, an arch is drawn so that it crosses the length DC at point F. The
AEFD rectangle is a golden rectangle (Table.3).
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Table3: geometrical analysis of Agha Noor Mosque of Isfahan. Source: authors
Comparing the results of the analyses
By comparing the results, we can conclude that through using geometry in the
mosques, first the outside and inside of the mosque have become separated
appropriately, and second it has caused prayer-sayers to enter the mosque’s
dome-house directly towards the Qibla. However, by following the general
principles of geometry and proportions of traditional mosques, we can create in
the users the feeling of pacing into a spiritual and religious place. The
traditional architect had focused on the presence of people in the space, and by
giving order to dark, half-bright and bright spaces, he has tried to conduct
people from one world to another (Fig.1).
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Fig.1: comparison of the geometrical analysis of mosques. Source: authors
Conclusion
Through analyzing three mosques of Safavid period in Isfahan (Imam Mosque,
Sheikh Lotfollah Mosque and Agha Noor Mosque), it can be stated that the
thing which is important in Iranian architecture is that the architect focuses on
creating and perceiving the spaces. In order to depict a spiritual space, the
Iranian architect has been at first visualizing space and thinking about how to
separate the addressee from the madding world, and during a special process,
enter him into another world. As can be seen in the architecture of Imam
Mosque in Isfahan, the addressee gradually enters the yard through two twisted
corridors which are located in the two sides of the northern porch; this can
depict passage from darkness to the light. The addressee would also observe the
seraglio’s entrance on the other side of the yard. In Sheikh Lotfollah Mosque,
the addressee passes through a corridor which twists 90o to the right and
gradually goes far away from the outside world and is prepared for entering into
another space and enters the dome-house space while he is standing in front of
the Qibla. In Agha Noor Mosque also the addressee enters into the yard from a
corner through a dark corridor, and on the opposite angle, he can see the gate of
entering into the dome-house. In all these three studied samples, by means of
geometry, the designer architect has created a space for the mosque, which can
make the addressee feel a spiritual sense and be prepared for entering into
another world.
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Endnote
1Geometrical method of drawing a golden ratio: in order to draw a
rectangle with golden ratio, we consider the CBGD rectangle. We find point A
in the middle of DG, and draw a circle with center A and radius AB. We extend
the line DG so that it crosses the mentioned circle at point E. The ratio of DE to
DC is the golden ratio, and the CFED rectangle is a golden rectangle (Fig.2).
DE/DC = 1.618
Figure2: golden rectangle. Source: authors
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