2018 Scienceline Publication

Journal of Civil Engineering and Urbanism

Volume 8, Issue 4: 44-53; July 25, 2018

ISSN-2252-0430

The Manifestation of Geometric Principles in the

Traditional Architecture of the Monasteries; Case Study:

Sheikh Shahab Al-Din Ahari Tomb and its Hidden

Geometry

Zeinab Nazer¹^and Ahad Nejadebrahimi²

Master of Architecture, Faculty of Architecture & Urban Design, Tabriz Islamic Art University, Iran

Associate professor of Tabriz Islamic Art University, Iran

^Corresponding author’s Email: z.nazer@tabriziau.ac.ir

ABSTRACT: The tomb of Sheikh Shahab al-Din Ahari was built in the 6^thcentury AH and its evolution has taken

place in the periods of the Ilkhani, Timurid, Safavid periods. Sheikh Shahab al-Din Ahari was the master of Sheikh

Safi al-Din Ardebili (the Safavid's father). Because of the Safavids, they had a special respect for him, And there are

manuscripts around the walls of the mosque of Sheikh Bahai, Shah Abbas III, Abolghasem Nabati, which shows the

significance of this monastery during the Safavid period and before it. The unique features of the architecture

suggest that the architect used the construction of geometric principles and the exact system of Iranian proportions.

And considering that the study of the geometry of the Sheikh Shahab al-Din Ahari monastery, the tomb since the

Ilkhanid era in East Azerbaijan, has not been carried out and because of the lack of clear exploratory resources some

researches required considering the importance of the subject, geometric proportional analysis approach that seek to

answer this question: which role geometry has played in the construction and development of the spatial elements of

the monastery? Therefore, the study of analytical research and data collection tool to collect data and information

have been used both field observations and library, and in order to revisit the geometric principles and proportions

in this collection, geometrical analysis was carried out using geometric analysis, plan, facade and sectional analysis.

The results of the analysis indicated that the architect of the building has had the required knowledge of the

geometrical proportions and geometry systems that has used theme in selecting the scale of the construction and

location of the main spaces, such as: large space under the dome (known as Ghosh khaneh), Chinese houses

(Chinikhaneh), courtyard, Eyvan (porch) with two minarets and two small booth of two sides of the floor. The

unveiling of hidden geometry in the design of the building reminds us of the privileged position of geometry in

traditional architectural design, which helps to better understand traditional architecture.

Keywords: Sacred, Geometry, Iranian, Architecture, Structural, Design.

INTRODUCTION

Din Ahari monastery (Pouraminian et al., 2014 ), and then

the importance of traditional architecture geometry that

was one of the most significant sciences that constituted

the statue of architecture and most designers used

geometric drawings as a scientific basis for their designs,

because from the originality of traditional view, they have

real aspects of eternity.

Eternity is achieved by means of communication

with a major goal through the world of eternal patterns

and following the rules of variety of traditional arts. An

artist who works within the tradition depicts his soul on

the outer world, and with this hypothesis, the writers

began to find hidden geometric relationships in this work,

and eventually with a great deal of effort they managed to

draw some geometrical relations in the design of the

building that it can be expected the designer of the

building also used such drawings to design this building.

The past Iranian architecture always has been inspired by

the use of geometry and accurate drawing methods, to the

extent that knowledge of the rules of mathematics and the

drawing and use of particular types of it was the duty of

any architecture. The distinction between architects and

their competition with each other was based on this basis.

Therefore, it is concluded that the geometry of Iranian

colonialism is important and the understanding of this

feature in contemporary architecture and the relevance of

the contemporary and tradition architecture are important

and it is necessary (Bowdzhani, 1990; Haji Ghasemi,

1995; Molavi, 2002 ). The authors with the knowledge of

the importance of geometry in the traditional architecture

began with this hypothesis that the design of this work

could not be formed without the use of geometry. At the

first, because of the importance of the Sheikh Shahab el-

To cite this paper: Nazer Z and Nejadebrahimi A (2018). The Manifestation of Geometric Principles in the Traditional Architecture of the Monasteries; Case Study: Sheikh

Shahab Al-Din Ahari Tomb and its Hidden Geometry. J. Civil Eng. Urban., 8 (4): 44-53. www.ojceu.ir

44

Geometry or proportional geometry is a sacred art

form due to its fundamental association with the

Creation's principal laws. The visual expression of the

order of these laws is best represented through the

discipline of geometry. Geometry is both quantitative and

qualitative in nature. Its quantitative dimension regulates

the order and construction of design forms. Its qualitative

nature sets the proportions of design forms and represents

an expression of the order of the universe as a visual

representation of the truth. Each figure or geometric

shape, when seen from the perspective of its symbolic

meaning, represents an echo of unity and a reflection of

the values and principles within the larger frame beyond

that unity (universal unity) (Ardalan and Bakhtiar, 2000 ).

Seyyid Hossein Nasr (2004) argued that geometry and

rhythm manifest a doctrine of unity which is central to

Islam, upon which Islamic art developed based on

mathematical ratios and proportions which represent the

very heart of Islam (Kritchlow, 1976 ).

Drawings in this research have been done through the

architecture software, AutoCAD. The compilation of the

materials in the theoretical discussions and the

introduction of geometry and proportions from published

researches on Islamic thought, such as the interpretation

of the Holy Quran and the books of Muslim scholars.

Geometric shapes drawings are based on the study and use

of the book: Iranian geometry from Abu al-Wafa

Bowdzhani (1990) and the treatise of Moftah al-Hasab

from Ghiasoddin Kashani. Pictures and drawings of the

building are provided by the authors. Then with

considering the structure of the collection in different

periods, and the importance of Ivan and Gonbadkhaneh,

these two architectural elements have been introduced as

the focal points of the building. And by assuming these

points for geometric drawings, In order to achieve the

geometry of the facade and the architectural plans for the

geometrical review was carried out to identify the

proportions set, and appropriate and acceptable responses

that provided a clear and coordinated process.

Geometry is the blueprint of the creation and the

generator of all forms. It is a science that deals with

numbers in space on four basic levels: the first one is

arithmetic (pure numbers), i.e., any measurement or

proportion is a geometrical measurement. The second

level is numbers in space which represent proportional

geometry. They reflect the meanings and “Ideas”. The

third level is numbers in time, which is the foundation of

music. The fourth level is numbers in space and time

which represent the cosmology of the universe. Geometry

explores and explains the patterns that unify and reveal

the structure of the Creation within all natural patterns of

growth or movement and their conformity with geometric

shapes. All life forms emerge out of timeless geometric

codes. Viewing and contemplating these codes allow us to

understand the wisdom of the inner workings of the

universe in order to fully comprehend and appreciate its

beauty based on the concept of proportions. Ikhwan Al-

Safa wrote, “One of our aims… consists of demonstrating

clearly that the whole world is composed in conformity

with arithmetical, geometrical, and musical relations.

There, we have explained in detail the reality of universal

harmony” (Nasr, 2004 ).

Main elements of architecture and affiliated arts

Geometry plays a fundamental role in design of

Iranian architectural monuments. From the viewpoint of

exterior functioning, the use of geometry as art for

creation of shapes, patterns and proportions reminds the

Great Architecture of the World and recalls the

Archetypes. From the viewpoint of interior functioning,

geometry as science for selection of structural dimensions

such as height, length and width of the building and its

structural elements governs the structural behaviour of the

building, the behaviour that follows the geometry. The

right geometry makes the building behave correctly.

In order to create harmony and create reasonable

proportions in the building, the index or source was

determined and all dimensions were subjected to it.

Peyman has been such an indicator in Iranian architecture

and modular architecture in European architecture. In this

architecture, Peyman focuses on living and space spaces, a

tool for adjusting dimensions and sizes, and the geometry

of the architectural guideline in providing discipline and

harmony (Omranipour 2005, 27 ). The third element in

architecture is a form. Pythagoras and his followers

believed there is a relationship between numbers and

forms. Islamic philosophers like the Muslim Brotherhood

also believed in the emergence of the universe based on

numbers. In their opinion, the intrinsic basis of this

universe is the number, and therefore the number that in

fact should be considered as pure quantity. But in this

thinking, the meaning of the number is not the values used

to measure physical quantities (Leveler, 1987 , 20 ).

In the presented paper, the authors attempt to clarify

the formation of building form and plan with the help of

geometric analysis. The universe was made to be the same

as the unseen universe, and everything that has been made

in this universe is a symbol of something in that world.

MATERIALS AND METHODS

The authors have used analytical method and information

gathering tool in the field of observation and library use.

To cite this paper: Nazer Z and Nejadebrahimi A (2018). The Manifestation of Geometric Principles in the Traditional Architecture of the Monasteries; Case Study: Sheikh Shahab

Al-Din Ahari Tomb and its Hidden Geometry. J. Civil Eng. Urban., 8 (4): 44-53. www.ojceu.ir

45

A quantitative aspect of geometry

Area (number)

Forms (form)

Geometry

measurement

scale

Qualitative aspect of geometry

Chart 1. Derivatives from Guenon, 1361, pp. 38-45

numbers

The primary three proportional roots √2, √3 and √5

Proportions

forms

Arithmetic, geometric and harmonic proportions

Circle, triangle, square, pentagon and shapes derived from them

Chart 2. Main elements of architecture and related arts (Tahabaz, 2004)

golden mean and the primary three proportional roots √2,

Geometric proportional systems

In architecture dating back to prehistory, particularly

in Islamic arts and architecture, the most important

geometric proportional systems are: the proportions of the

√3 and √5, on which all Islamic arts and architectural

forms, especially their geometric pattern design, are

based.

Table 1. Some geometric principles used in the architecture of the monasteries (authors)

The main

elements of

geometry in

architecture

The

geometric

order used in

the building

component

Description with an example

The golden mean proportion is a proportional system whereby two elements are related to each other

by a set proportion. Two segments of a line not equal to each other are related in a proportion:

a/b=(a+b)/a (Figure 1). It is this unique point that divides the single line into segments with

qualitative proportions. It is a reflection of multiplicity within unity in terms of geometry. If the line

is divided into equal halves, the two segments would be a monotonous repetition of one and the

same thing, neither multiplicity nor unity within the geometry.

Golden

proportions

Figure 1. The golden mean proportion: a/b=(a+b)/A=1.61803.

The root

proportions

based on the

square.

The geometric

order of plan

and facade

Proportions

Figure 2. The successive constructions of the root proportions in proportional rectangles based on

the diagonal of the square.

The ratio of

the lateral

side to the

radial side is

2

The geometric

order of the

facade

Figure 3.

To cite this paper: Nazer Z and Nejadebrahimi A (2018). The Manifestation of Geometric Principles in the Traditional Architecture of the Monasteries; Case Study: Sheikh Shahab

Al-Din Ahari Tomb and its Hidden Geometry. J. Civil Eng. Urban., 8 (4): 44-53. www.ojceu.ir

46

Geometric

order and

decoration

Twelve

Figure 4. Geometry analysis of the View of the Sheikh Lotfollah Mosque in Isfahan

(Haji Ghasemi, 1995)

The geometric

order of plan

and facade

Eight

Figure 5. In the above drawing, we divide the circle into eight equal parts. If we connect these

points to the adjoining points, we will surely have a regular octagon. Now, if we connect points, two

to two, four to four, and six to six, then two nested squares are obtained. The resulting octagon is

related to Islamic architecture and arts.

Special

numbers

Geometric

order of

facade and

decoration

Six

Figure 6.

The geometric

order of plan

and facade

Square

Which are inside a circle

Figure 7.

The geometric

order of plan

and façade and

decoration

forms

The circle

Figure 8. The geometries examined above include circular geometry.

The geometric

order of plan

and facade

Triangle

Figure 9. The geometries examined above are triangular geometry.

To cite this paper: Nazer Z and Nejadebrahimi A (2018). The Manifestation of Geometric Principles in the Traditional Architecture of the Monasteries; Case Study: Sheikh Shahab

Al-Din Ahari Tomb and its Hidden Geometry. J. Civil Eng. Urban., 8 (4): 44-53. www.ojceu.ir

47

Geometry Analysis at Sheikh Shahab al-Din

Ahari Monastery

Using geometry in design can be considered from

two perspectives: 1. Finding important points and places

in a way using geometric drawings, which is the main

theme of the analysis in this article. These drawings can

be studied in two levels in general. The first level involves

the appearance of geometric shapes along the way. Like

squares, octagons and regular polygons visible in plan,

facade and detail. The second level analyzes geometric

designs that determine the dimensions, direction and

comonomy of previous levels, and are not at first sight.

Using geometric drawings to obtain the values and

proportions that determine the dimensions and proportions

of the organs of the structure and its components, as seen

in Egyptian and Greek architectural works. These

drawings generally result in numerical results such as √3,

√2, golden ratio, etc., and then these numerical ratios

appear in dimensional forms. In this paper, we will look at

this type of analysis as a sub-topic.

Figure 12. Vertical section A-A Source: East Azerbaijan

Cultural Heritage Organization

Documents for hidden geometric order, at the first is

performed on a three-dimensional model with considering

the plan, view and cross-section simultaneously. The use

of AutoCAD software eliminates the need for maps with

variety of scales and increases the accuracy of the

drawings.

Figure 13. North View, Source: East Azerbaijan Cultural

Heritage Organization

Geometry in the facade

The first form that attracts the attention is the golden

ratio. The length of the ABCD square is approximately the

width of the main porch and the other side of the square

(BC-AD) to the vertex curve. By drawing the DE curve

into a square diameter radius (BD), we see the golden

proportions on the front of the main monument of the

tomb, also by drawing the EK arc in the ABEF

rectangular radius, the proportions of the end point of the

main view K are obtained and, similarly, these proportions

are visible in the small stands of the two floors of the

faces of the GADJ and in the exterior of the Booths.

Figure 10. The Monastery Plan, Source: East Azerbaijan

Cultural Heritage Organization

Draw 1. Golden proportions in the main facade of the

monastery (North) Source: authors

Referring to the radical proportions 2 in the table,

taking into account the middle of the inscription of the

porch (O) and drawing the peripheral circle and

connecting O to E and F, the line segment BC becomes

radical 2 times the segment AB and CD of the connection

The point O is obtained at the H point (the end of the

Figure 11. 3D vision, Source: East Azerbaijan Cultural

Heritage Organization

To cite this paper: Nazer Z and Nejadebrahimi A (2018). The Manifestation of Geometric Principles in the Traditional Architecture of the Monasteries; Case Study: Sheikh Shahab

Al-Din Ahari Tomb and its Hidden Geometry. J. Civil Eng. Urban., 8 (4): 44-53. www.ojceu.ir

48

line). Also, from the intersection of the OB line with the

peripheral circle, the point K is obtained, which specifies

the edge of the minaret.

Draw 2. Eyvan ratio to side frames is Radical 2. Source:

authors

Draw 4. The geometric analysis of the monastery facade

has proportional proportions resulting from the division of

the circle of the circumference of the face into 12 parts,

Source: authors

Preliminary drawings are required before the other

key points are obtained. The first is drawing the

equilateral triangle which represents the regular size of the

facade, including the sides of the sides AB, BC, CT.

And then draw the triangles equilateral triangle by

drawing the FBD Shamse we have six hexagon ABCDEF

environment FBCE rectangle like the picture. The vertex

O corresponds to this hexagonal on the Avon inscription

center. It is very common to draw a six-slice with this

orientation in traditional Iranian architecture. For

example, the 6-point basis for finding the optimum Ron

(Pirnia, 2008, 136) is also a hexagonal base for drawing

the Iranian golden rectangle (1): √3 And the intersection

of AC and BD on minarets along the center line and the

intersection of M and N coincide is an AC, DF, AE, DB

with rectangular FBCE, rectangular porch environment

F'B'C'E 'achieved.

We obtain the GHIK rectangle from the 90 degrees

rotation of FBCE rectangle and the intersection of the

sides reveals the main points of the view. Refer to the

method shown above for the entire view, by extending the

12-edge geometry on the porch, appear the main points of

the vault and the inscription.

Draw 5. Eyvan (porch) geometric analysis monastery

proportional ratios divided by the circle into 12 parts,

Source: authors

Draw 3.

Draw 6. Geometric analysis with respect to triangulation.

Source: authors

To cite this paper: Nazer Z and Nejadebrahimi A (2018). The Manifestation of Geometric Principles in the Traditional Architecture of the Monasteries; Case Study: Sheikh Shahab

Al-Din Ahari Tomb and its Hidden Geometry. J. Civil Eng. Urban., 8 (4): 44-53. www.ojceu.ir

49

Draw 7. The proportional ratios obtained by dividing the

circle into 8 parts, Source: authors

Draw 10. Geometric analyzes with respect to

triangulation Source: authors

Draw 8. Geometric analysis of faces with respect to

triangulation, Source: authors

Geometry on the plan

Draw 11. Geometric analysis of the facade with respect to

the regular octagon Source: authors

The geometry of the golden proportions in the plan

was based on the drawing of the square to the center of the

large mosque ABCD and the drawing of the CG arrow to

the square diameters (AC), the proportions of the main

porch (rectangular BGHC) and the Chinese houses around

the Grand Mosque (DCEF). Similarly, golden proportions

can be deduced from the yard of the JIFL, the MNOP

small mosque and the courtyard booths.

Geometry of decorations

One of the specialties of the Sheikh Shahab al-Din

Ahari monastery is: On the sides of the eastern side, two

flowers are carved into a gray stone piece. Two flowers

consisting of "two parallel triangles" and a pyramidal

circle that also corresponds to geometry in the main

facade of the tomb.

Draw 9. Geometric analyzes with respect to symmetry

Figure 14. The eastern side of the Sheikh Shahab al-Din

Source: authors

Ahari tomb Source: authors

To cite this paper: Nazer Z and Nejadebrahimi A (2018). The Manifestation of Geometric Principles in the Traditional Architecture of the Monasteries; Case Study: Sheikh Shahab

Al-Din Ahari Tomb and its Hidden Geometry. J. Civil Eng. Urban., 8 (4): 44-53. www.ojceu.ir

50

Figure 18. Sample of sign on the Tombstone in the

Sheikh Shahab al-Din tomb, Source: Authors

Figure 15. Sample of hexagram of the eastern door in the

Sheikh Shahab al-Din tomb, Source: Authors

Figure 19. sample of sign on the Tombstone in the Sheikh

Shahab al-Din tomb, Source: Authors

RESULTS AND DISCUSSION

The point in the Sheikh Shahab al-Din Ahari monastery

and the monuments of the period and the subsequent

periods is the significance of the sixth figure in the

proportions and decorations that are clearly visible on the

tombstones in the museum's decoration of a hexagram or a

six-star filled in the eastern entrance door.

The same figure is on the sides of the entrance to the

tomb of “Sheikh Heydar Meshkin shahr” related to the

period of 7th and 8th AH and on the tombstones of the

“haft tanane Kalkhouran”, in the courtyard of the Sarabi

Mosque, most of which are monuments such as graves

and tombstones, and the mosque and tomb to "Advar

Ilkhani "is attributed. In addition, the Hexagram or six

stars has an old role in the architecture of the Mogul and

Ilkhan. The coins of the Ilkhan period are of particular

importance to researchers in terms of the variety of

content and patterns of information they bring.

Figure 16. Decorative sample in Sheikh Shahab al-Din

tomb, Source: authors

The coins of the Ilkhan period are of particular

importance to researchers in terms of the variety of

content and patterns of information they bring. Coins are

an important part of archeological documents and

evidence for the clear gray aspects of the history and

civilization of the ancient nations and peoples. Since the

content of the coins has since been devised to reflect the

culture, art and religion, social and political relations, the

Figure 17. Sample of sign on the Tombstone in the

Sheikh Shahab al-Din tomb, Source: Authors

To cite this paper: Nazer Z and Nejadebrahimi A (2018). The Manifestation of Geometric Principles in the Traditional Architecture of the Monasteries; Case Study: Sheikh Shahab

Al-Din Ahari Tomb and its Hidden Geometry. J. Civil Eng. Urban., 8 (4): 44-53. www.ojceu.ir

51

economic situation, the language and the customs, the

customs and cultural geography of different lands and the

precise and undeniable sources of periods of human

history and culture. That evidence show the presence of

the star of David in the center of coins, the doorway to the

monasteries and in decorations, shows the support of

Jewish religion towards Islam during this period.

analyzing geometric proportions is one of the most

important and fundamental issues of traditional

architectural research, which is less archeologically

considered, and for the creation of works that are the true

continuation of valuable architectural paths, the first step

is to get proper and adequate knowledge of it and its type

of architecture.

The current study aimed to find out the geometry of

Sheikh Shahab al-din Ahari Monastery by its designer.

The aim was to readout geometry and the proportions of

the main facade (the north facade) and the architectural

plan and decorations. The result showed that the architect

has had knowledge about the systems of alignment and

geometric drawings, since in finding the architectural

elements in the plan, the layout of the architectural

elements in the plan, the fit between the architectural

spaces and the creation of decorations on the basis of

principles Geometric and excellent proportions.

In recognition of the geometry of the building, a

regular

twelve-dimensional,

regular,

octagonal,

hexagonal, triangular, and accurate golden proportions in

plan and facade are praised and golden proportions and

Iranian proportions are in perfect development with each

other that have been merged.

DECLARATION

Authors’ Contributions

All authors contributed equally to this work.

Considering the evolution of the monastery in

different periods, in the architectural dimension, it is

closely related to the proportions and geometry of the plan

in the eastern part, where the tomb plan is perfectly

symmetrical in the northern axis of the south. And the

most striking architectural feature of the extension of the

patriarch can be found in these cases are: to adopt a kind

of space commitment in merging new and initial segments

with the application of pre-considered geometric

principles, observance of the fit between the dimensions

of the spaces according to the principles of standing

together with the fit between the spaces and considering

the performance of these spaces to meet the physical and

mental needs of its users, and on the other hand, with

regard to the arrays in the courtyard, workstations on the

west side of the courtyard, which are completely different

from the east side of the east side, make it possible to

attribute the original body of the tomb to this section.

Therefore, with regard to the architectural extension

of the building and the recognition of the main elements

of this architecture, we have chosen the focal points as the

default for achieving the structural geometry of the

building, and the regular twelve-dimensional geometric,

octagonal and golden proportions in the drawings process

are reasonable and fitted to the resulting, and then aligned

with the view of the building. In recognition of the

geometric shapes of the building, a regular twelve-

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To cite this paper: Nazer Z and Nejadebrahimi A (2018). The Manifestation of Geometric Principles in the Traditional Architecture of the Monasteries; Case Study: Sheikh Shahab

Al-Din Ahari Tomb and its Hidden Geometry. J. Civil Eng. Urban., 8 (4): 44-53. www.ojceu.ir

53