International Journal of Mathematical Research

2016 Vol. 5, No. 1, 1-24.

ISSN(e): 2306-2223
ISSN(p): 2311-7427
DOI: 10.18488/journal.24/2016.5.1/24.1.1.24
© 2016 Conscientia Beam. All Rights Reserved.

MATHEMATICAL & SPATIAL RELATIONSHIP BETWEEN DOME AND AL-

MOUSALA IN CONGREGATIONAL MOSQUES (AN ANALYTICAL STUDY
OF BASIC DIMENSION OF CENTRAL DOME PATTERN)

Raeed Salim Ahmed Al-Nuamman1

1
Lecture, Mosul University, Department of Architecture, Iraq

ABSTRACT
Islamic architecture has a clear impact for systems and the relationships of Mathematical and Geometrical
proportions , which reflected in their buildings. The research will deal with an important aspect that linked
in two mains elements in the Congregational Mosques. The first is a house of prayer (Al-mousala) as the
main and most importantly space in the mosque, and the second is a dome as structural and decorative
element, who was significantly associated with Congregational Mosques later. This study is one of very few
studies which have investigated the kind of the Mathematical& Geometrical proportions relationship, also
the spatial linking of these two elements with each other's. Through the statistical analysis that links the
relationship between their different dimensions and the positioning kind of the main dome on a house of
prayer (Al-mousala). For this purpose the resaerch has been selected two sets of samples. The first models
include a different regions of Islamic Congregational Mosques represent different patterns of
Congregational Mosques as a sample of general Islamic architecture while the second comprises a number of
Congregational Mosques in Mosul city, a representative of the local architecture.
Keywords: Central dome, Al-mousala, Congregational mosques, Mathematic, Islamic architecture, Ottman
architecture, Mousl mosques.

Received: 18 December 2015/ Revised: 1 January 2016/ Accepted: 5 January 2016/ Published: 8 January 2016

1. INTRODUCTION
Mosque is the Islamic term was not known before the advent of Islam. The mosque is every
place that we can worship the Allah. Mosque high place among architectural installations may
not be an exaggeration to say that the mosque architecture is the foundation upon which the
other buildings. though the buildings of mosque begun simple far from complexity as the first
mosque was a square piece of land surrounded by a fence and it was the roof afford columns of
trunks of palm trees or movable columns from other buildings, as in the Great Mosque in Sana'a

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 International Journal of Mathematical Research, 2016, 5(1): 1-24

about (6 AH) and the Mosque of Basra (14 AH) and the Mosque of Kufa (17 AH) and the Mosque
of Amr Ibn Aas (21 AH). the planning of Prophet's Mosque has delat al-qibla and sahen with
others arcades become a main source to successive generations of architects in the east and
west of the Islamic world with addition of some amendments which were taken from the local
style in each region until appeared the Olaiwana planning with appearance of the school, which
consists of an open courtyard surrounded by four Iwans facing each other where this style
together become as an nucleus to build mosques from the fourth century AH / tenth century.
Then appeared the third style , which consists of two part the first prayer house which upon it a
huge dome surrounded by half-domes , the second is an open courtyard surrounded by corridors
this style appeared since the second half of the seventh century AH / third century AD [1].

2. THE DOME
The oldest domed building found in the late Uruk and the beginning of the era GONODA in
the Royal Cemetery in Ur (Sumerian era around the third millennium BC) [2]. originated domes
in ancient Egypt and Iraq ancient, it has materials in Iraq by using bricks in construction , after
that its moved to Greek architecture then to all the world .
the Dome covers a square area based on four walls, then dome moved to the Romanian
architecture in temple Alkol Seyou in Rome, and it moved to Christian architecture as a dome
above structure , also was a model of the churches was contains a number of domes above the
nave. After that it moved to the Islamic architecture, Dome of the Rock in Jerusalem-Sharif is
considered as the most important dome in Islamic architecture.

2.1. The History of Dome in Islamic Architecture

The first Islamic domes is the Rock Dome in Jerusalem, Figure (1), it return to the era of
the Umayyad (661-750 AD), built by Caliph Abdul Malik bin Marwan year 72 AH, with octagon
shape. the rib length 20.95 m, and a height of 31.5 m, the dome is composed of two layers, the
upper wooden covered with sheets of lead and doctrine copper plates in above (Ibn Al-
Atheer,1375 AH,P86) , then appeared several environmental and functional factors led to use of
this element but in a small scale , did not indicates the high of ceiling almousla for a number of
reasons, including providing currency and materials needed for this type of construction and
increase space capacity without columns and usefulness in reference to the site of al- imam or al-
Khatib in Congregational mosques . The oldest example of the Iraqi domes still exists is the
Dome of Ukhaydir palace dating back to the first half of the second century which are found in its
corners Hnaya pluteaceae, while the al- salibiea dome in Samarra is oldest dome of a grave at the
time of the Abbasid al-Mustansir 246 AH. while The Dome of Aleppo is the oldest dome in the
belad alsham, which date back to the year 336 AH [3].

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Figure-1. Perspective section in the Dome of the Rock

2.2. Types & Forms of Domes

2.2.1. The Conical Domes
This type of domes are used since the mid-fifth century and even the Ottoman period in The
shrines , In it the dome rises high to indicate the status of the deceased and its importance. this
type of domes build by gypsum and enveloped from the outside by stone. Al- salibiea dome is the
most famous of these domes (the tomb of a Muslim) (Figure 3) in Samarra, which is domes of the
Abbasid period, it is the first shrine in Islam, and includes the remains of the caliphs: ( al
montaser, almuhtadi &almutaz).

Figure-2. plan and perspective to the salibiea dome

2.2.2. String Domes

This type of domes made from gypsum , and often be fragile so it covered by second dome to
protect it from environmental conditions. It has half structure curvature be structure from
crisscross tendons, begin from indented base and contain twenty four part intersect. the curved
tendons is to change from the square or ribbed base to apse base by a series of cubic or
prismatic mocarnasat with different shapes. like the dome of Al-Nouri mosque, and usually built
by white gypsum around the dome center to form a star has Several heads [4].

2.2.3. Half Circular Domes

Domes built as a half circular in Egypt and Syria in one direction in the Fatimid period and
two direction in the sixth century and then added plaster ornament in their bases during the
Ayyubid period and increased the height neck of dome in Almamalik period .

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2.3. Different Types of Dome Forms

There are different types of domes in Egypt except half circular, elliptical , ribbed and
wooden as the Dome of Sheikh Abdullah in Cairo, which carrying in highest a small ribbed dome
, while in the countries of the Maghreb have prevailed dome spherical half without foreign
decorations, while I took forms domes in Persia elliptical shape covered by Al-qachani

Figure-3. A variety form domes in the Islamic world

2.4. The Construction of the Dome and it Relates to the Al- Mousala
The dome loads transmitted to the ground by supports solid stone and various forms
including square, circular octagonal or other forms. Often contain cavities like niches or other
details. The Dome that has a ring section settle either on a square rule or octagonal According to
the structural system used in the transfer of weight to the land where the almusala under it . there
are three structural systems for the transition from the square to the dome circle which are as
follows [5].

2.4.1. Al-haniat Corner

The second innovation for the transition from a square plan to Octagon then to the ring it
is al-hinea corner It is the cone suppression has head vertical angle is placed on his side that
divided the vertical corner angle. meaning that its base half a circular has been placed in head
level and it ribs half cone are placed in a horizontal plane, so that applies in every corner of the
its two straights sides on the two angle ribs of the square region will be covered by a dome, but
the domes, which convert the square plan to the octagon or circle by the corners heniat it have
found in the palaces of the Sassanids, and found examples of corner heniat units in al-Ukhaydir
Palace including the dome of main entrance, and appeared in the al- amaa door in al-aljosag
Khaqani palace in Samarra, .the examples of henaya corner domes al- hakim Mosque and the
Dome of the seven girls mosque Figure 4 illustrates these elements [6].

Figure-4. Al- Hneayat corner (Dome mihrab of Kairouan Mosque)

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2.4.2. Spherical Triangles

The spherical triangles was Used as an element in stone domes in Jordan and spread its use
depending on the expansion in the use of domes and semi- domes, thanks in it innovation to
Arabs, they have been used to move from square plan to round plan to support the lower edges
of the domes. it have been used a lot in the colonies of the Byzantine Empire , this structure
construction allows to rise the dome with lightness and save costs, opposite most of the old ways
that have been used in the Pantheon. considered the dome of the "Aea Sophia" mosque is the
first example of this, And continued in the Islamic era where it found a dome of Amra palace bath
and in al- sarh bath . the diameter of the spherical triangles either be equal to the diameter of
dome, In this case the triangles look like part of the dome, or can be the diameter of spherical
triangles are not same the diameter of Dome even it can work the dome from half sphere
completely, Figure 4 illustrates these elements [7].

Figure-5. Spherical triangles (Blue Mosque in Istanbul)

2.4.3. Al Mogrnasat
Al mogrnasat considered developer type from the Hanaya corner form , it invented, as a construction
element to transfer the plan of the dome from square to circle plan , where it was the first appearance of it
in Persia in the cemetery Junbada doorin gorgan in Iran. it have been mushroomed rapidly with the end
of atheist century, and the first model consist of from two direction as a first stages of the evolution of Al
mogrnasat, and consists of two direction, the first one is include three Kosrat and second include one, so
Al mogrnasat have been used as a constructed element and found in the domes of the Fatimid in Mashhad
al-Jaafari and Atkp and Mrs. paper also found in the monastery of the martyrs the presence in this dome
represent manifestation of the spread of the Fatimid architectural elements in contemporary Christian
architecture [6]. Figure 6 illustrates these elements.

Figure-6. Al mogrnasat

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2.5. The Dome Use in Islamic Architecture and its Relationship to the Al- Mousala
The dome used in various Islamic buildings, especially mosques addition to its use in schools,
palaces and baths as well as the use in the conical dome particularly in roofing shrines and
scenes. Islamic architecture distinguished by using an unlimited number of domes in mosques and
put it in different locations of the mosque. This domes take its titles of their location within
mosque or Al- mousala as a following is of these sites. [8]

2.5.1. Al- Mihrab Dome

In this case, one dome in the mosque located above the mihrab and on the axis direction of al-
qibla, it has been commonly used in all the mosques of the Islamic world as in the Al-Aqsa
mosque of in Figure (7)

Figure-7. Al-Aqsa mosque

2.5.2. The Lobby Dome

The Mosque contains the second Dome at the end of mihrab tile in the edge of al- saucer
called the Dome of the lobby, where Use this method in the mosques of the Maghreb and Egypt,
it a duplicate of the al-mihrab Dome for prayers in sides of mosque, like in the Al-Al-azhar
mosque, [9] and in the Zitouna Mosque of Kairouan. As in Figure (8).

Figure-8. Zitouna Mosque and Azhar mosque

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2.5.3. The Central Dome

In addition to structural solution the central dome in Islamic architecture represented the
large dome of the sky as they are in many Islamic mosques as the Ottoman mosques is a good
example of this type of mosques like Selimiye and Sulaymaniyah mosque as in Figure (9).

Figure-9. Sulaymaniyah mosque and Selimiye mosque

3. HOUSE OF PRAYER (AL- MOUSALA)

The Islamic fuqh shows the Prophet sunat give basic mosque components. The Prophet's
Mosque select the basic components of a mosque (the fence, saucer, a house of prayer or (AL-
mousala) , canopy, corridor, the position of the muezzin), and so has identified the prophetic
elements of the mosques pattern of that have affected to the different patterns in the shape and
style of expression [10].

3.1. Legitimacy Laws for the Design House of Prayer Space (Campus) and the Election of
its Shape
The House of Prayer (AL- mousala) is the primary design element in the mosque, it was to
the noble sayings of prophet greatest impact in determining the AL- mousala shape and it's the
primary and secondary elements and has placed several concepts and foundations to design the
space and shape of the house of prayer (AL- mousala) as following:

1. Straight and Wide

The Prophet Mohammed Peace be upon him said "settlement their rows from the perfect of
the prayer " (Bukhari and Muslim) [10] that’s means the virtue of the first row in prayer and that
the increase row length will increase the number of believers therefore necessary the shape of
AL- mousala to have rectangle. the long rib facing the al-qibla wall.so that from better left the
shape like as circle and octagon where decreasing rows toward the direction of al-qibla [11].

2. Lighting and Visual Link with the Outside Space

Based on the words of the Prophet, peace be upon him (beware of paying attention in prayer,
the pay attention in prayer is fault.

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So, the windowing within the internal space will affect categorically on its function during
the prayer, so prefers the lack of windows in the level of view worshipers, particularly in the qibla
wall or the side walls, so as not to distract worshipers during prayer or hear the sermon. It is here
determined by the visual extension of the internal space to be from the top and not of aspects,
nature of activity prayer preference for non-contact on the horizontal plane between the inner
space and outer space, and be a visual extension of the upper contact is the closest to the internal
space [11].

3. Functional Flexibility
The inner space of the mosque dedicated to pray and that only require place vector to al-
qibla. The multi functionality of the mosque since Mosque of the Prophet, peace be upon him did
not change anything in its architectural program. al- mousala or house of prayer is remained a
flexible space that can fit and flexibility fully with any other function is the place to prayer and
it's the same place to receive where science students were sitting front and around the teacher
,and a court hall where the judge sits is in front of the audience [11].

4. HUMANE ISLAMIC ARCHITECTURE

Islamic architecture characterized a number of humanity characteristics and principles in its
buildings that recorded by researchers in Islamic architecture and these principles

4.1. Human Scale

Islamic architecture respects human scale. The "God" prefer the human creature that
generosity from the rest of the creatures and regarded him as a supreme value. Ibn Qutaiba was
the first to talk about human scale in Islamic architecture," represent the house jerseys " Where
tailored shirt by owner size, the house also built by static scale, the foundation purpose of
architecture is to achieve serenity and confidence to those who hold this architecture, whether
public or private, the basic principle is the rights and needs and ambitions [12]. Islamic
architecture characterized by simplicity and respect for human scale, the first mosques prevailed
starting from the Prophet's Mosque and the mosques of Basra and Kufa expressive of human
thought and the Muslim believer away from the luxury and richness of Greek temples or gothic
churches first mosques crossed honestly Islamic values for monumental that have emerged in the
last centuries. As Graber suggests that Islamic culture is not (object oriented) object-oriented, but
find meaning in the act and sound (al-athan) more than sight [13].

4.2. Directionality and Axial

Directionality has two dimensions (intellectual, ideological) and (kinesthetic, visual).
Directionality one of the most important Islamic architecture features, where all the faithful have
directional to the Kaaba and this trend means to achieve unity of purpose as directional reflected

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in the mosque through a clear line movement from the entrance to the mihrab. Where we see in
each expansion of the mosque the place of entrance change to keep the directionality of the
mosque and the movement from entrance to the Al-mihrab. In addition to the presence of
decorative elements on the internal inter face of the campus reflects the direction of direction as
well as in the dome of Al- mihrab to indicate the directionality.

5. STRUCTURAL ELEMENTS IN THE PRAYER HOUSE (AL- MOUSALA)

5.1. Masts and Columns
The roof of Prophet's Mosque carries on the trunks of palm trees, and preferably reduce the
number and size this trunks to not being cut the ranks of worshipers and hinder follow-Khatib
during a Friday sermon [14].

5.2. Al- Mousala Roof

Roof of the Prophet's Mosque has low level and this suna has remained for centuries. The
Arab style was the lowest in rise in addition to the Andalusian-style no more than a few meters
high in al- masala. With the emergence of ions were dashed this suna especially in east of Islamic
world after twelfth century, for example, rising house of prayer in the mosque of Isfahan reached
35 meters high, while the rise of( al- mousala) in the Ottoman-style mosques like Sulaimaniyah
more than 50-meter [14].

5.3. The Dome

That the construction of a dome in the mosques did not raise the objection of Muslim
Scholars of different sects as the niche and minarets which was rejected by some scholars of the
nation [14]. The domes began Small size, in the first centuries appropriate and proportionate to
mosque scale, then evolved dramatically to become the size of the dome more than the size of a
house of prayer in mosques as models Seljouqe and Ottoman mosques, especially after the second
century AD.

6. PREVIOUS STUDIES
This Study Contributes in the Existing Literature as the Following

6.1. Hassan [11] The (The Properties of Design Thinking in the İnternal Space of the
Mosque)
The Study had been aimed mainly to clarify the characteristics of architectural thought to the
process of designing the internal space of the mosque and its various elements, the study mainly
relied on the analytical method, with these elements rating in four basic elements. Simplicity
without complicated, the functionality not formality, and compatibility do not contrast. the most
important findings of the study, that thinking in the design of the internal space of the mosque is

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the process of restricted in certain controls and the problem of design has been distinguished by
simplicity, not complex, the study do not care to the relationship between the dome and the
House of Prayer (al- mousala). [11]

6.2. Al- Jubouri and Samaan [15] (The Study of Geometric Properties in Islamic
Architecture)
The study aimed to analyze the shape bases in the architecture of mosques and dealt with
two elements (dome and the House of Prayer al- mousala) by studying and analysis of the
correlation of each of it with the rest mosque parts. the study focused in some engineering
characteristics that bind these two elements with each other without focusing on the nature of the
mathematical relationship between them [15].

6.3. A Ardalan and Laleh [16]

The study addressed the mosques in the Muslim world by detail, the study has been divided
Islamic world into eight distinct regions have been isolated from researcher eight components of
the mosques elements, namely, (the yard, al- mousala, the entrance, the mihrab, the dome, the
corridors, the terrace, places of ablution) in this the study had been isolated these elements from
buildings that have been altered by the Muslims to mosques by adding these items to those
buildings. the study do not care to the relationship between the dome and the House of Prayer
(al- mousala) [16].

6.4. Al-Umari and Hafsa [14] (The impact of Islamic Religion in the Formation of
Buildings Urbanism)
The study dealt with in one of the chapters (Chapter 5) The provisions of the design of the
mosque focused on perceptions of typical design space to (prayer house (al- mousala)) and the
provisions of the construction of the dome in the Islamic mosques .The study in this chapter had
been develop a set of influential restrictions to the election of the appropriate form for this space
based on a set of legal provisions in most of them derived from the Hadith The study pointed to
the dome is as a complement element to the roof of a house of prayer (al- mousala) . However the
aims of study is not looking of at the relationship between the dome and house of prayer or the
nature of the mathematical relationship between them [14].

6.5. Al-Maliki and Kbila [17] (Geometry and Mathematics in the Arab-Islamic
Architecture)
The study( the geometry and mathematics) dealt with the phenomenon of proportionality in
Arab-Islamic architecture ,, as a phenomenon evident in the different civilizations, the study
define three types of proportions (mathematical, and geometrical and to harmonization ) in
Architecture from the approved rules in Islamic architecture. The study provided theoretical

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framework to promote its goal (make contemporary architecture aligned with the cultural
heritage). through the vocabulary addressed by trying to provide a theoretical reference depend
on it the design decisions on it , that handles Architects contemporaries to create a
contemporary Arab architecture has the same expressive characteristics to Islamic architecture
through a thorough understanding of the concept of draw inspiration from the inherited
architecture, The first chapter of the study focused on the concept of (mathematics and geometry
in architecture engineering , The second chapter cared to examine architecture and
proportionality explaining confiscation and determine their impact in determining the intent or
spontaneity in proportionality and devoted the third chapter for the study of Islamic architecture,
focusing on the production of the Abbasid architecture) for the period specified in the study,
while the fourth chapter specialist to analytical and practical study, The study Despite the
comprehensiveness and coverage of several aspects but it did not studied mathematical
relationship between the elements of the dome and the house of prayer (al- mousala), in the
Congregational Mosques, but he can be considered the goal of the current search a tributary into
the general aim of the study.
From this Previous studies and the research it has identified the research problem as follows
(what is the specify the nature of the mathematical relationship between the dome and the house
of prayer in Congregational Mosques).
This study is one of very few studies which have investigated in this research problem.

7. SEARCH GOAL
This study uses new estimation methodology aims to crystallization a part of the specificity
of Islamic architecture by providing scientific and accurate identification of the nature of
mathematical relationship between the dome and the House of Prayer (Al- mousala) in the
congregational Mosques
Identify specific reach and certified proportion to the size of the dome to the size of a house of
prayer (Al- mousala).
Identify the dimensions of one of the research variables by knowing the dimensions of the
other, through reaching of a mathematical formula linking the variables of research. A
contemporary architects can be adopted this formula to create a congregational mosques have
the same expressive characteristics of Islamic architecture through a thorough understanding of
the concept of inspiration from the legacy architecture.
The paper contributes the first logical analysis to the mathematical relationship between the
dome and the house of prayer in Congregational Mosques.

8. RESEARCH HYPOTHESIS AND REQUIREMENTS PRACTICAL STUDY

To achieve the objective of this research has been the development of a hypothesis include
the following.

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There is a clear relationship between the size of the dome and the size of a house of prayer in
the congregational Mosques and the strength of this relationship varying according to the
mosques patterns.
Variation the relationship associated with between the positioning of the dome for the house
of prayer (Al- mousala), according to the pattern of Mosques

9. PRACTICAL STUDY
9.1. Define the Variables
Topical variables knew this relationship by two variables each representing a qualitatively
compared to occupy their possible values
The first variable represents "domes number" within the house of prayer (Al- mousala) and
identified the following values. No Dome, one Dome, two domes (of equal size, is of equal size),
more than two domes (of equal size, is of equal size)
The second variable is the position of domes within the house of prayer (Al- mousala) and
identified the following values. Centralized, decentralized (above the mihrab, at the back, in both,
on the porch of direction, domes scattered, matrix above the sanctuary) Al- Jubouri and Samaan
[15]
Mathematical variables included the relationship between size of the dome and size of
prayer house (Al- mousala) it has been calculate through available dimensions for these two
variables to the mosques falling within the research sample.

9.2. Sample Selection Search

In order to test this hypothesis necessitated study and analysis of a sample of an elected
mosques, university buildings in various Islamic regions with a focus on mosques buildings in the
local architecture. The following considerations into account when electing the study process
models This study documents must be a high degree of accuracy in documented elected
architectural models , which is a very important factor as it was elected buildings mosques
University, which has a high degree of accuracy and descriptive documentation attached models
record and schemes minutes. Try to choose models for different Congregational Mosques and
Islamic models covering most regions and for a period of time characterized by widespread urban
development. On this basis, has been elected the following Congregational Mosques models as a
sample and study the process as shown in Table (1) and Figure 10 shows the horizontal plans of
these buildings.

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Table-1. List of models as a sample and study

architectural year of
No site Style Reference
project achievement
AL- Kairouan multi-columns
1 Tunisia 836 AD . [18]
Mosque (Arabic)
Umayyad Damasc multi-columns
2 705-715 AD . [18]
Mosque us (Arabic)
multi-columns
3 Zitouna mosque Tunisia 731 AD . [18]
(Arabic)
shaah Isfahan four iwan 1072-1092
4 Iran) [19]
mosque (Sjawqa) AD
Al- shareefe multi-units 1437-1447
5 Turkey . [18]
mosque (Ottoman) AD
Süleymaniye central dome 1550-1557
6 Turkey [20]
Mosque (Ottoman) AD
central dome 1569-1574
7 Selimiye mosque Turkey [20]
(Ottoman) AD
8 Shah Zada central dome
Turkey 1454-1458m [21]
mosque (Ottoman)
Sultan Ahmed central dome
9 Turkey 1616 AD [20]
Mosque (Ottoman)
office
Prophet Grgise
10 Iraq central dome 1158 AD construction
mosque
engineering.1983
office
Mujahid AL-din
11 Iraq central dome 1133 AD construction
mosque
engineering.1983
office
12 Al-agwat mosque Iraq central dome 1702 AD construction
engineering.1983
13 Alrabaah mosque Iraq central dome 1694 AD [22]
14 Khuzam mosque Iraq central dome 1576 AD researcher
office
15 Jamshid mosque Iraq central dome 1560 AD construction
engineering.1983
office construction
16 Basha Mosque Iraq central dome 1755 AD
engineering.1983
Source: The researcher

AL- Kairouan Mosque

Umayyad Mosque

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shaah Isfahan (SECTION PLAN) Zitouna mosque

Sultan Ahmed Mosque PLAN Selimiye mosque PLAN

‫مققبةطع في ال‬ ‫مخطط أفقي‬

PLAN Al- shareefe PLAN Shah Zada mosque

mosque

Süleymaniye Mosque PLAN

SECTION Prophet Grgise mosque PLAN

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Figure-10. Architectural models elected to study the process schemes

10. RESULTS
10.1 Results Related to the Position of the Dome above the Prayer House
10.1.1 Results Relationship the Domes Number Above House of Prayer
The results did not indicate the similarity between the mosques patterns in the research
sample for this relationship. While the central dome pattern distinguished only one dome above
the house of prayer. While we find in the four iwan pattern distinguished more than two dome
above the house of prayer. While the multi-column pattern ranged between only one dome above
the house of prayer, as in the Umayyad Mosque or two domes as in Kairouan mosque and al-
zetwona mosque.

10.1.2. The Results of Domes Location above the House of Prayer

The results pointed to the similarity between the central dome pattern with four iwan
pattern in the position of main dome dominant in the center above the house of prayer center and
their different with multiple-column pattern. also we find a difference in the position of the
number domes in the same style of the mosque for the last while, we find repositioning the Dome

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of the one above the entrance in some mosques as Umayyad mosque, we find others mosques
belonging to the same pattern in which positioned domes, one above the entrance while the other
above the mihrab, as in al- zetwona mosque, and Table (2) build the above results.

Table-2. Relationship (local) between dome and almousla

Relationship (local) between dome and
almousla
Position in almousla No. of dome

Two dome
centeral
other

more
Un

One dome
centeral

No one
Irregular domes

Above entrance

style Architectural project

Above mehrab
Row above

Equal size

Equal size
Not equal

Not equal
In sides
haram

both

◙ ◙ Milt column AL- Kairouan Mosque 1

◙ ◙ Milt column Umayyad Mosque 2
◙ ◙ Milt column Zitouna mosque 3
◙ ◙ Four iwan shaah Isfahan mosque 4
◙ Central dome Al- shareefe mosque 5
◙ ◙ Milt unite Süleymaniye Mosque 6
◙ ◙ Central dome Selimiye mosque 7
◙ ◙ Central dome Shah Zada mosque 8
◙ ◙ Central dome Sultan Ahmed Mosque 9
Central dome Prophet Grgise
◙ ◙ 10
mosque
Central dome Mujahid AL-din
◙ ◙ 11
mosque
◙ ◙ Central dome Al-agwat mosque 12
◙ ◙ Central dome Alrabaah mosque 13
◙ ◙ Central dome Khuzam mosque 14
◙ ◙ Central dome Jamshid mosque 15
◙ ◙ Central dome Basha Mosque 16
Source: The researcher

10.2. The Results of the Mathematical Relationship between the Dimensions of the Dome
and the House of Prayer (Al-Mousla)
For the purpose of accuracy in calculating the size of the domes being different shapes,
mosques included in the sample has been used to represent the house of prayer and the main dome
of each mosque by an (Autocad) program and then calculate the size of the dome and the size of a
house of prayer for each collector.

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 International Journal of Mathematical Research, 2016, 5(1): 1-24

Figure-11. Represent the models of the research sample by Autocad program

Source: The researcher

Table-3. Shows the specific of search data, which represent dimensions the physical of the Dome and its counterpart in

the House of Prayer (Al-mousla)

Al-mousla dimension house of prayer Dome dimension in
Architectural
No. Style Length Width High Size Diameter High Size
project
m m m M3 m m M3
AL- Kairouan Milt
1 70 38 20 48000 12 9 769.5
Mosque column
Umayyad Mosque Milt
2 139 37 26 133718 16 19 1889
column
Milt
3 Zitouna mosque 59 29 14 23954 12 16 536
column
shaah Isfahan
4 Four iwan 66 40 27 71280 20 23 14407
mosque
Al- shareefe Central
5 66.5 43.5 14 40498 24.1 12 3613.8
mosque dome
Süleymaniye
6 Milt unite 69 63 22 95634 25.72 18.8 21540
Mosque
Central
7 Selimiye mosque 60 45 25 67500 31.5 23 235662
dome
Shah Zada Central
8 43 34 19 35131 18.42 18 6139
mosque dome
Sultan Ahmed Central
9 72 64 25 70225 23.5 25 2850
Mosque dome
Prophet Grgise Central
10 21 10 9 1890 9.5 7.25 385
mosque dome
Mujahid AL-din Central
11 25 10 8.5 2125 13.6 8.9 470
mosque dome
Central
12 Al-agwat mosque 24 12 7 2016 9.6 4.5 448
dome
Central
13 Alrabaah mosque 23 11 7 2070 19 7 1100.8
dome
Central
14 Khuzam mosque 15 7 5.5 577.5 5 4 144.25
dome
Central
15 Jamshid mosque 17.4 9.5 7.25 1189 3.78 3.75 297.25
dome
Central
16 Basha Mosque 29.3 14.5 10.85 4562 11 10.5 1120.5
dome
Source: The researcher

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 International Journal of Mathematical Research, 2016, 5(1): 1-24

The statistical analysis of research data set in Table (3) by SPSS software showed the
following results.

10.2.1. Results of Relationship between Dome Size and Size of a House of Prayer ( Al-
Mousla)
● The relationship between size of the dome and size house of prayer( Al-mousla) for
the sample as a whole is non-linear relationship and can be calculated the size of dome from the
size of a house of prayer( Al-mousla) by the following equation.
The weak correlation coefficient and also shows in Table (4)

Table-4. Correlation of relationship between size of the dome and size house of prayer as a whole
Dependent Mth Rsq d.f. F Sigf B0 B1 B2 B3
VAR0004 LIN .868 12 78.96 .000 3.6583 .001
VAR0004 LOG .862 12 74.99 .000 -7.3876 2.1715
VAR0004 QUA .927 11 69.61 0.00 2.8816 .0028 -2.E-
07
VAR0004 CUB .959 10 77.85.61 .000 1.9254 .0061 -1.E-
06
VAR0004 COM .755 12 36.91 0.00 3.495 1.0002
VAR0004 POM .94 12 188.24 0.00 .5579 .3494
VAR0004 . .341 12 6.21 .028 1.9041 -24.161
VAR0004 GRO .775 12 36.91 .00 1.2514 .0002
VAR0004 EXP .755 12 36.91 .00 3.4952 .0002
Source: The researcher

● The relationship of the dome size with house of prayer( Al-mousla) size in mosques
central dome style for all mosques belonging to this style , was linear but it is not clear and the
following equation enables us to calculate the size of the dome by the size of the House of Prayer(
Al-mousla) with incorporeal weak degree .
For more analysis separate the mosques of this style into two groups, one representing
mosques of local architecture and the other outside the scope of local architecture as the following
results.
1.The relationship between size dome to the size of the house of prayer( Al-mousla) in
mosques pattern central dome (local architecture) and a clear and distinct from the rest of
relationship patterns,. The following equation enables us to calculate the size of the dome by the
size of the House of Prayer. with high correlation coefficient equal 0784 figures were , and as that
shown in Table (5) and chart (1)
Z = (58.144+0.24 X
Where X represents the size of house of prayer ( Al-mousla)
Z size of dome

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 International Journal of Mathematical Research, 2016, 5(1): 1-24

Table-5. Relationship between size the dome to the size of the house of prayer in mosques pattern central dome (local

architecture)
Unstandardized Coefficients Standardized Coefficients
Model t Sig.
B Std. Error Beta
1 (Constant) 58.144 201,375 .791 .289 .784
VAR00001 .247 .085 2891 .034
Source: The researcher

Chart-1.

2.The relationship between size dome to the size of the house of prayer( Al-mousla) in
mosques pattern central dome (out of local architecture) accepted with correlation coefficient
equal 0.462 , The following equation enables us to calculate the size of the dome by the size of the
House of Prayer and as that shown in Table (6) and chart (2) .
Z = 32.8 + 0.18 x
Where X represents the size of house of prayer ( Al-mousla)
Z size of dome

Table-6. Relationship between the size of dome to the size of the house of prayer in mosques pattern central dome

Coefficients-a.
Unstandardized
Standardized Coefficients
Model Coefficients t Sig.
B Std. Error Beta
1 (Constant) 32.842 39.033 .248 .841 .462
AR000012 .695 1.567 .443 .688
a Dependent Variable: VAR000011

Chart-2.

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 International Journal of Mathematical Research, 2016, 5(1): 1-24

10.2.2. Results the Relationship between High of Dome and Rising House of Prayer ( Al-
Mousla)
● The relationship between height of the dome and rising house of prayer( Al-mousla) to
the sample as a whole the level of non-linear relationship , calculated the high of dome by the
rising of house of prayer( Al-mousls) by the following equation as it is shown in Table (7).
H = 11.129 – 5.63EX+ 0.31E 0.2 X
Where X represents the high of house of prayer ( Al-mousla)
H height of dome

Table-7. Correlation of relationship between height of the dome and rising house of prayer as a whole
Dependent Mth Rsq d.f. F Sigf B0 B1 B2 B3
VAR00005 LIN .277 12 4.61 .053 5.2879 .4094
VAR00005 LOG .256 12 4.13 .062 -1.943 5.2042
VAR00005 QUA .316 11 2.54 .125 11.1295 -5.634 .0313
VAR00005 CUB .501 10 3.34 .063 013.947 6.13525 -,4819 .0115
VAR00005 COM .343 12 6.26 .028 4.0008 1.05070
VAR00005 POM .386 12 7.53 .016 1.639 .6937
VAR00005 . .438 12 9.37 .010 2.9816 -7.8115
VAR00005 GRO .343 12 6.26 .028 -1.5392 .0495
VAR00005 EXP .343 12 6.26 .028 6.662 .0495
Source: The researcher

● The relationship between height of the dome and rise of house of prayer( Al-mousla) to
the sample as a central dome style is non-linear relationship , calculated the high of dome by
the rising of house of prayer( Al-mousla) by the following equation as it is shown in Table (8).

Table-8. Correlation of relationship between height of the dome and rising house of prayer as a central dome style
Dependent Mth Rsq d.f. F Sigf B0 B1 B2 B3
VAR00013 LIN .833 8 39.9 .000 1.4635 .6560
VAR00013 LOG .847 8 44.25 .000 011.043 8.70062
VAR00013 QUA .843 7 18.78 .002 01.2477 1.1085 -.0144
VAR00013 CUB .894 6 16.89 .002 -13.48 4.734 -.3218 ,0073
VAR00013 COM .657 8 15.34 .004 3.308 1.0744
VAR00013 POM .700 8 28.43 .001 .6982 1.028
VAR00013 . .841 8 42.2 .000 3.2503 -10.884
VAR00013 GRO .657 8 15.34 .004 1.1964 .0717
VAR00013 EXP .657 8 15.34 .004 3.3083 .0717
Source: The researcher

● The relationship between height of the dome and rise of house of prayer( Al-mousla) to
the remainder of sample is non-linear relationship , calculated the high of dome by the rising
of house of prayer( Al-mousla) by the following equation as it is shown in Table (9).
H= 50,57-5.15X2-0.152X3

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 International Journal of Mathematical Research, 2016, 5(1): 1-24

Where X represents the high of house of prayer (Al-mousla)

H height of dome
The results of the relationship between Diameter of dome and width of house of prayer (Al-
mousla). The relationship between diameter of the dome and width of house of prayer (Al-
mousla) to the sample as a whole the level of non-linear relationship.

Table-9. Correlation of relationship between height of the dome and rising house of prayer
Dependent Mth Rsq d.f. F Sigf B0 B1 B2 B3
VAR00015 LIN .253 2 ,68 .497 21.8846 -.4622
VAR00015 LOG .389 2 1.27 .378 35.1832 -7.7462
VAR00015 QUA .997 1 187.14 .52 .50.5733 -5.1530 .1525
VAR00015 CUB .997 1 187.14 .52 .50.5733 -5.1530 .1525
VAR00015 COM .188 2 .40 .593 20.5091 .9718
VAR00015 POM .288 2 .81 .464 50.7157 -.5091
VAR00015 . .387 2 1.26 .376 2.0164 6.9694
VAR00015 GRO .166 2 .40 .593 3.0209 -.0286
VAR00015 EXP .166 2 .40 .593 20.5091 -0286
Source: The researcher

The relationship between diameters of dome to the width of the house of prayer (Al-mousla)
in mosques central dome style is a clear and distinct from the rest of relationship styles,.
The following equation enables us to calculate the diameter of the dome from the width of
(House of Prayer). With high correlation coefficient equal 0.638 but deviated from that AL-
Selimiye mosque figures were, and as that shown in Table (10) and chart (3)
R = (x-3.996) / 1.882
Where X represents the width of house of prayer ( Al-mousla)
R reduce of dom

Table-10. Relationship between Diameter of dome and width of house of prayer) in mosques central dome style

Coefficients(a)
Standardized
Unstandardized Coefficients
Model Coefficients t Sig.
B Std. Error Beta
1 (Constant) -3.966 8.170 .792 -.485 .638
VAR000013 .1,882 .459 4.097 .002
A Dependent Variable: VAR000010

Chart-3.

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 International Journal of Mathematical Research, 2016, 5(1): 1-24

11. CONCLUSIONS
11.1. The Conclusions Associated in the Position the Dome above the House of Prayer (Al-
Mousla)
In the mosques types (Seljuk and Ottoman) (central dome and four iwan) clear similarity in
of the number of domes above the house of prayer and places of repositioning those domes over
the prayer house (Al-mousla) and disagreement with the Arab type, possibly due to the local
Architecture effect it prevailing in those areas.

11.2. Conclusions Related in the Mathematical Relationship between the Dimensions of

the Dome and the Dimensions of the House Prayer (Al-Mousla)
The results confirmed the hypothesis of research relating to the existence of a clear
mathematical relationship between the dimensions of the dome and the dimensions of the house
of prayer (diameter dome / width a house of prayer, the size of the dome / size of house of
prayer) in the mosque, the Congregational Mosques, however, this relationship was confined in
the mosques of the Ottoman style only , whether that it built in their original environment (the
Ottoman Empire) or in neighboring countries environment (Mosul), which indicates the
originality the proportions in the Ottoman architecture without effect it in local architecture
prevailing. on the other hand there are indicates to the natural effect to this architecture on the
rest of its neighboring countries, especially neighborhood countries, the fact that architecture is a
symbol of the Islamic caliphate, and depending on the results of ratio of the dome rise to the
rise of house of prayer . the research distinguish between from the mosques of the Ottoman type
(style central dome) two kinds, the first has a global attributes, as a edifice , which is mosques
built in the Islamic Caliphate site, this is the fact that architecture is a mirror that reflects the
state's power and prestige of hand and the great attention given by the Ottoman Empire for
building mosques on the other hand, and another variety of mosques in Mosul has attributes
local that reflect the humanitarian nature of Islamic architecture. And thus it can be identified
two kind of mosques style central dome based on the mathematical dimensions of the house of
prayer or the dome. The first is represents the Ottoman mosques (the central dome style) of a
global nature, which has achieved an acceptable relationship between the geometrical dimensions
to the variables of the research. The second is the Ottoman mosques (central dome style) have a
local nature and which has a strong mathematical relationship between the basic geometric
dimensions of the variables Search.
The previous classification refers clearly to the apparent disparity in the conditions and
possibilities for the emergence of these two types:
The first is dominant within the urban fabric helps in making the mosque as a dominant
element within the fabric. thus the mosque built within wide and open spaces as well as the
used construction materials available helped to open of standard dimensions, and this case to
reach its peak in the Selimiye Mosque which explains deviance in Dimensions dome of

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 International Journal of Mathematical Research, 2016, 5(1): 1-24

Selimiye from those in the sample While the second kind harmonious within the organic fabric ,
local environmental. constructed by simple materials , so the basic dimensions of geometric
harmonious with the surrounding fabric and proportionate to the humanitarian character of
Islamic architecture.
 The Search gives to (architectural designer) possibility to calculate the diameter and the
size of the dome depending on width and size of the House of Prayer(Al-mousla) , in
mosques ( central dome style) that want to design newly or those need to be
rehabilitated, by based on the mathematical equation mentioned above, can be to the
specialists to use that equation to validate elemental ratios ( dome and the house of
prayer (Al-mousla) ) in the mosque when re-restored.
 By knowing the size and diameter dome from size and display house of prayer (Al-
mousla)from the previous equations can be to the professionals specifically architects,
definition of the mosque dome shape as ( semi-circular or semi-circular or semi-
circular shaped ) by changing the height of the dome while retaining dimensional basis.
 Characterized by the Dome of the Selimiye Mosque from the rest of the Ottoman
mosques in the size and height of the dome which confirms the edifice form of the
mosque on one hand and the relentless pursuit of architect Sinan to exceeded the
dimensions dome of Mosque Hagia Sofia from other side.

12. RECOMMENDATIONS
Studied the mathematical relationship between the other elements in the Congregational
Mosques like the dome and the minaret and others.

Funding: This study received no specific financial support.

Competing Interests: The authors declare that they have no conflict of interests.
Contributors/Acknowledgement: All authors contributed equally to the conception and design of the study.

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