Available online at www.sciencedirect.com
of design proce
Loai M. Dabbourn
Department of Architectural Engi
Received 24 June 2012; received in
time they mediate between the two poles of order and diversity
as well as among different
relationship between cosmology and geometry is manifested in
Islamic patterns where
universal language, constituting one of the most important
multicultural symbols in design.V. All
relations of magnitudes such as points, lines, surfaces, orPeer
review under responsibility of Southeast University.
Frontiers of Architectural Research (2012) 1, 3803912095-2635
& 2012. Higher Education Press Limited Company. Production and
hosting by Elsevier B.V. All rights reserved.solids in space and
the way the parts of a particular objectt together (Concise Oxford
English Dictionary, 1999).Geometry is well known based on two Greek
words geo,meaning the earth, and metry, meaning to measure.
The word geometry refers to the science of properties and
nTel.: +962 796978940.
[email protected],[email protected]& 2012. Higher
Education Press Limited Company. Production and hosting by Elsevier
B.rights reserved.geometry acts as the vocabulary underpinning the
pattern language. These ndings supportthe argument that geometry
was independently discovered and applied by Islamic culture as
aesthetic levels. This paper analyzes geometric principles and
design features of traditionalIslamic patterns, involving geometric
proportion analysis. It also describes the syntheses ofIslamic
patterns from the perspectives of Islamic cosmology, philosophy and
metaphysics ofgeometry, which can be seen as following a
pre-established principle of geometric andproportional design with
high accuracy and great precision. Furthermore, the
underlyingIslamic patternsss for Islamic geometric patterns
neering and Building Systems, Alzaytoonah University of Jordan,
Amman 11733, Jordan
revised form 23 August 2012; accepted 24 August 2012
AbstractThis paper discusses geometric proportions which serve
as a design tool, especially for Islamicpattern design. The key
role of geometry in Islamic patterns is discussed with relation
toproportions which act as the underlying structure of the design
process. Evaluations based onspatial structure and esthetic
criteria are integrated into the conceptual phase of the
designprocess. Proportions serve two objectives; rstly, in pattern
design, proportions are stronglylinked to geometry, which can be
viewed as a self-guiding method of esthetically proven
design.Secondly, geometric proportions regulate primarily the order
of patterns; while at the sameGeometric proportions: The underlying
So geometry literally means the measurable earth orearthly
measurements. Geometry, according to Plato,can also refer to the
science of stereo-metry or spatialmeasurements. The very laws of
how things are allowed tobe by the Divine will are the laws of
Harmony of Being.Tradition holds that, as engraved over the
entrance toPlatos Academy, Only he who is familiar with
geometryshall be admitted here (Critchlow, 1976).
Geometry has existed in many buildings and design formsacross
centuries. The rst conrmed record of geometricknowledge and its
relationship to astronomy, human and
Geometric proportions 381music can be traced back to the ancient
Greeks, inparticular, Pythagoras and Plato. However, prior to
theGreeks, many old civilizations have left clear
geometricfootprints by applying sacred geometry in their
construc-tions. The prehistoric carved stones found in
Scotlandrepresenting the Platonic Solids.1 can be dated back toover
a thousand years earlier than the Greeks.2 The Greeksmay well have
been the rst to have offered geometry tothe public, but they were,
by no means, the rst to realizeit (Critchlow, 1987; Hecht, 1988;
Geometric ratios and proportions existed and wereemployed in the
design of ancient sacred and ceremonialsites in all traditional
civilizations. They were invariably builtwith dimensions that
incorporate mathematical numbers,constants and ratios such as the
golden/sacred mean,and the use of geometries based on proportional
roots,proportional rectangles and Pythagorean triangle
(Pennick,1994). For example, Christian cathedrals incorporated
sym-bolic geometry, while the design of Hindu and Buddha templeswas
based on sacred geometry. In Islamic art, geometricelements have
been employed since its origin and were usedto create unique
geometric formations, serving as the under-lying structure of
Islamic design process.
Geometry or proportional geometry is a sacred art formdue to its
fundamental association with the Creationsprincipal laws. The
visual expression of the order of theselaws is best represented
through the discipline of geometry.Geometry is both quantitative
and qualitative in nature. Itsquantitative dimension regulates the
order and constructionof design forms. Its qualitative nature sets
the proportionsof design forms and represents an expression of the
order ofthe universe as a visual representation of the truth.
Eachgure or geometric shape, when seen from the perspectiveof its
symbolic meaning, represents an echo of unity and areection of the
values and principles within the largerframe beyond that unity
(universal unity) (Ardalan andBakhtiar, 2000). Seyyid Hossein Nasr
argued that geometryand rhythm manifest a doctrine of unity which
is central toIslam, upon which Islamic art developed based on
1The Platonic solids are the names given to the ve
three-dimensional solidstetrahedron , hexahedron, octahedron,
dode-cahedron, and icosahedrons(perfect shapes) formed when
divid-ing a sphere based on the exact shape and angle. For the
Greeks,these ve solids were the core patterns of physical creation.
Theywere seen as the archetypal patterns behind the four
elements(earth, air, re, and water), while the fth was held to be
thepattern behind the life force itself, the ether.
2Small carved stones found in Scotland conform to the vePlatonic
solids, which suggest an association with this
mathematicalprinciple.mathematical ratios and proportions which
represent thevery heart of Islam (Critchlow, 1976).
Geometry is the blueprint of the Creation and thegenerator of
all forms. It is a science that deals withnumbers in space on four
basic levels: the rst one isarithmetic (pure numbers), i.e., any
measurement orproportion is a geometrical measurement. The second
levelis numbers in space which represent proportional geometry.They
reect the meanings and Ideas. The third levelis numbers in time,
which is the foundation of music. Thefourth level is numbers in
space and time which representthe cosmology of the universe.
Geometry explores andexplains the patterns that unify and reveal
the structureof the Creation within all natural patterns of
growthor movement and their conformity with geometric shapes.All
life forms emerge out of timeless geometric codes.Viewing and
contemplating these codes allow us to under-stand the wisdom of the
inner workings of the universe inorder to fully comprehend and
appreciate its beauty basedon the concept of proportions. Ikhwan
Al-Safa wrote, Oneof our aimsy consists of demonstrating clearly
that thewhole world is composed in conformity with
arithmetical,geometrical, and musical relations. There, we
haveexplained in detail the reality of universal harmony(Nasr,
Geometric proportions in architectural patterns repre-sent a
design language, as words do in a spoken language.They determine
the frameworks within which elements maybe arranged into a pattern,
a relation between one elementand another, and a proportional
relation within one ele-ment. They address and reect the natural
laws that governthe basic harmonies of nature, being describable by
meansof mathematics and geometry.
Islamic art favors geometry because of its intelligibleaspect.
Geometry possesses abstraction and the capacity toexpress and
reveal objectively immutable and spiritualtruths. Geometry involves
proportions and prime roots thatare considered the most beautiful
proportions (the propor-tions of beauty). As such, beauty, for the
Muslim artists, isobjective and self-expression of truths, which is
the essen-tial nature of beauty as Plato stated, Beauty is
thesplendor of the truth (Burckhardt, 1987).
The language of Islamic design springs primarily from
theabstract. Therefore, geometry in general and
geometricalproportion in particular carry great importance in the
designprocess of Islamic art, presented in its primary
elements,geometry, biomorphic forms, and calligraphy, which are
allbased on and ruled by the underlying geometric
laws(proportions). It follows that the Islamic design principlesare
reected in geometry. In other words, geometry plays acentral role
in Islamic design.
This paper examines Islamic pattern design, which can beviewed
as a key method of expressing Islamic cosmologicalesthetics. In
addition to representing cosmological andphilosophical structures
at the level of form, geometricpatterns can also be seen as efcient
and powerful repre-sentations of some of the central concepts that
characterizeIslamic debates on the divine nature. Islamic pattern
wasdeveloped as visual tools for contemplating the
underlyingmathematical nature of the universe, leading to the
natureof beauty, by virtue of Gods creation of the universe
(thenature of the divine itself).
2. Geometric proportional systems
In architecture dating back to prehistory, particularly in
comprehend the order and harmony inherent in the Crea-tion. It
is the visual representation of the mathematicalpatterns found
everywhere in man, nature, and cosmos.These patterns, with their
esthetic and philosophicalvalues, are found within all aspects of
The understanding of geometry as an underlying part ofour
existence is nothing new. In fact, the golden mean and
L.M. Dabbour382Islamic arts and architecture, the most important
geometricproportional systems are: the proportions of the golden
meanand the primary three proportional roots O2, O3 and O5,on which
all Islamic arts and architectural forms, especiallytheir geometric
pattern design, are based.
The golden mean proportion is a proportional systemwhereby two
elements are related to each other by a setproportion. Two segments
of a line not equal to each otherare related in a proportion:
a/b=(a+b)/a (Figure 1). It isthis unique point that divides the
single line into segmentswith qualitative proportions. It is a
reection of multiplicitywithin unity in terms of geometry. If the
line is divided intoequal halves, the two segments would be a
monotonousrepetition of one and the same thing, neither
multiplicitynor unity within the geometry.
The proportional rectangles or the proportional roots arebased
on the geometry of the polygons.
For example, the square includes O2,3 the hexagonincludes O3,
and the pentagon includes the golden meanwhich numerically equals
to [(O5+1)/2]=1.61803 (Figure 2;Hambidge, 1920; El-Said, 2001)
Figure 3 shows the successive constructions of the
rootproportions in proportional rectangles based on the diagonalof
The Muslim artists created these geometric proportionsfrom the
circle of Unity. As one of the most common shapes innature, it was
reected symbolically in the signs of theCreation, just like the sun
being one of the signs of divinity(the universal symbol) (Guenon,
1995; Figure 4). The circle isan obvious example of a basic
geometry, constituting all theproportional geometries inherent in
The circle of Unity is the most signicant form, for itcontains a
circumference revolving around a xed center. It istherefore
extremely important to understand that all othergeometric shapes
can be determined from a circle, fromwhich come the full polygons,
including series of roots andproportions. Figure 5 shows a symbolic
relationship betweenthe absolute and the relative, represented by
two circlesoverlapped. This construction is known as the Vesica
Pisces.The realm enclosed within this overlap is, according
toFrithjof Schuon, the Relatively Absolute (Schuon, 2003).The
absolute represents the metaphysical and the relativerepresents
illusion. The geometric proportions within theRelatively Absolute
sphere indicate that it is connectedto truth. The Vesica Pisces is
one of the key starting blocksfrom which sacred geometry was
applied in the geometricmatrix used for the design in all religious
Within the Vesica Pisces realms, the primary proportionalroots,
i.e., O2, O3, and O5, as well as the golden mean, areillustrated,
all of which are found within the realm of theRelatively Absolute.
When the drawing is further inter-sected by straight lines, an
equilateral triangle, a hexagon,a pentagon, a square and so on,
The sacred mean or Phi (), the divine proportion, andalso golden
section or golden ratio, is one of the key-stones
3O2 proportion is that of the internationally used A
papersizesA4 , the most commonly used, being 210 mm 297 mm.of
sacred geometry. The mathematics of the golden ratioproportion is
generated by the formula (O5+1/2) (or1:1.618).
The mathematics of the golden ratio is related to
LeonardoFibonacci, the founder of the Fibonacci sequence, a
nume-rical series found frequently in the natural world
(Lawlor,1989). It simply follows the rule that the next number is
thesum of the previous two numbers, as follows: 1, 1, 2, 3, 5,
8,13, 21, 34, 55, 89, 144 etc. If we divide any number in
theFibonacci sequence by the one before it, for example 144/89,or
89/55, the answer is always close to 1.61803, which is thevalue of
the golden ratio. The Fibonacci sequence, or thedescription of the
golden mean features can be seen every-where in the forms of
nature, music, and the arts. One of themathematical products of the
sacred mean is the spiral,commonly found in nature (Rawles, 1997;
Schneider, 1994;Figure 6).
Proportional geometry regulates primarily the order ofdesign
process. It is needed to create the micro cosmos bywhich we
acknowledge beauty in design forms. The beautyof proportions is
based on the simple geometry of regularpolygons with a set of
ratios of side lengths to diagonals(such as O2, O3, O4, O5 andy),
which can be translatedinto the design process.
These geometric proportions are used to quantify esth-etic
qualities. This process is, to a great extent, based onobjective
facts. Judgments on beauty versus ugliness can bebased on
systematic arguments characterized by unifyingprinciples or
patterns. They can be achieved by means ofalgorithms of visual math
as an objective ground which canbe founded on geometry and
proportions, which are part oftheir elementary pillars. As
Aristotle stated, beauty is tomaintain the just measure (Lawlor,
1989). Beauty inproportions has a key function in constituting them
becauseit forms the underlying structure of order versus
diversity,establishing systematic design principles.
The objective criteria of beauty revealed by means ofgeometric
analysis aim to establish sets of design tools,which would
increase, rather than restrain, the freedom ofdesign, and to nd a
system path to a design language thatincludes beauty rather than
systematically excludes it.
3. Geometry in man, nature, and cosmos
Geometry is an unseen presence in Islamic art and archi-tecture.
It is the visual means by which human mind can
Figure 1 The golden mean proportion: a/b=(a+b)/A=1.61803.
Geometric proportions 383Figure 2 The proportional roots: (a)
the O2 proportion, (b
Square 2 3
2 3 4Figure 3 The root propoother forms of geometric proportions
can be seen imbeddedin man, nature, and the universe, either
represented asmicro or macro cosmos.
Since ancient times, there has been a deep interest informs that
are considered to incorporate within theirintrinsic relationships
mathematical and geometrical pro-portions (universal truth). It was
believed that thesegeometries were derived from the basic laws of
theuniverse. Kepler stated the belief that geometry is
under-pinning the cosmos, which was based on Platos ideas thatGod
created the universe according to a geometric plan-God geometrizes
continually (Lawlor, 1989). The structureof the universe is
determined by and revealed as certainmathematical and geometric
constants which represent aconrmation that proportions are the
underlying fabric ofnature. This can be seen in man, nature, and
cosmos.Beyond this discipline, it was believed that these
geome-tries were based on the Creation itself (sacred) and,
byincorporating them in music, art and architecture, the fruitsfrom
these elds would have a harmony of proportions and aspecial sacred
characterharmony of being. By studyingor contemplating these
geometric proportions, an under-standing could be obtained towards
the sacred truth.
Figure 4 Unity in multiplicity and multiplicity in unity
primarycircle symbolizing wholeness, completion, unity and
Geometric proportions are one of the denitive geometricqualities
of life itself. According to the Holy Quran, man haswithin himself
all what is reected in the universethe bestproportions. Man is the
core of Gods creatures; he possessesthe most harmonious
proportions, reecting of the Divineharmony of being (Lings, 1976;
Guenon, 1994). We haveindeed created man in best of
formsproportions (The HolyQuran, Chapter 95, verse 4). Leonardo da
Vinci illustrated themathematical proportions of human body,
showing thathuman being exhibits clearly golden mean proportions in
5ns based on the square.e O3 proportion, and (c) the golden mean
(Phi) proportion.body based on ratios of 1.618. The Vitruvian Man
drawn byLeonardo Da Vinci is based on Vitruvius, who had written
thathuman proportions should have a relationship in
architecture.Vitruvius believed that if human proportions could be
incor-porated into buildings, they would become perfect in
theirgeometry. According to Vitruvius, the distance from ngertipto
ngertip should be the same as that from head to toe. Thesacred mean
rules can be seen in the ratios of body partsthroughout the human
body. Man reects these principles in alanguage of sacred geometry
(Guenon, 1995; Figure 7).
According to Robert Lawlor, The human body contains in
itsproportions all the important geometric geodesic measures
andfunctionsy the proportions of ideal man are at the center of
acircle of invariant cosmic relationships (Lawlor, 1982).
The study of geometric proportions has its roots in thestudy of
nature and matter (Skinner, 2009). Many formsobserved in nature can
be related to geometry. Forexample, the snowake crystals and honey
cells constructhexagonal geometries. Radium crystal and sound
vibra-tions that carry sound information are based on
O2proportions, showing the octagonal geometry. Flowers in
L.M. Dabbour384nature tend to have a variety of geometries,
althoughtheir variety seems to be innite. Four, ve, and sixpointed
geometries seem to be more common in nature.There are many plants
and other aspects of nature whichexhibit the form of spiraling
geometry, which is related toFibonacci proportions based on the
golden mean. Thus thegolden mean is the ngerprint of the Creation
Figure 5 Roots and the golde
Figure 6 Spirals, the mathematical products of
Figure 7 Vitruvian man, with proportions ba3.3. Cosmos
The mathematical harmony of the universe can be seenfrom the
proportions of the planets in our solar system. Forexample, the
ratio of the sacred mean can be seen in therotations of the Venus
and the Earth around the Sun in thatfor each ve years that the
Earth rotates around the Sun,
n mean within the Vesica.
Fibonacci sequence and the sacred mean.
sed on the sacred mean (Critchlow, 1976).
Geometric proportions 385the Venus rotates around it eight
times. The connectionbetween 5 and 8, both of which are Fibonacci
numbers, isthe golden mean proportion (8/5=1.6). The result of
thismotion is that the Venus draws a pentagon around thesun every
eight years (Skinner, 2009; Figure 9A).
Figure 9B shows that a circle is drawn, which representsthe
Venus mean orbit. A pentagon is constructed inside itand a small
circle placed through the arm-crossing points.The radius of this
small circle divides the radius of the largeone into golden
sections and can be used to space the
Figure 8 Geometric proportioVenus orbit from the Earths orbit.
It can be seen from theagreement between eightfold and vefold
geometries thateight touching circles are drawn from the Venus
meanorbit. In turn, the circumference circle is enclosing
theseeight circles, dening the Earths mean orbit (Martineau,2001;
The conclusion from these diagrams shows that, mathema-tically
speaking, the ratio of the mean orbits of the Venuss tothe Earth is
O2 proportion. The geometric representation ofthese orbits creates
the golden mean proportion.
ns in nature (Singer, 2008).
The same proportions can be observed between the Earthand the
Mercury. Two circles dened by the arm-crossingpoints of the
pentagon are both the Earths and theMercurys mean orbit. Their
sizes are their relative physicalbodies (Martineau, 2001; Figure
Sacred geometry describes the assertions of a mathematicalorder
of the intrinsic nature of the universe. Scientists see thesame
geometric and mathematical patterns asarising directly from natural
principles. Traditional art hasrules that apply to cosmic laws and
universal principles.(Schuon, 1984)
These and other similarities are seen in sacred geometryto serve
as the further proof of the cosmic signicance ofgeometric forms.
Islamic architecture is created based onthe essential harmonies of
nature together with varioussymbolic meanings and theories of
perfect proportions. Thedesigners based their geometrical
vocabulary on what theyhave seen in the nature around them, in an
attempt todevelop a codied series of proportions which may
improveour psychological comfort with buildings (Skinner,
It has been proposed that the understanding of sacredgeometry
was extended into time and space. We may neverknow for sure whether
such geometry was identied rstfrom the observation of natural
formations, or alternatively,it came as a result of an intellectual
quest. However,whichever it would be, it is clear that these
mathematicalcodes derived from nature began to be applied in the
designof many important man-made structures.
Geometry constitutes a graphic description of the uni-verse.
Geometric analysis is an attempt to understand the
causes and the reality of the nature, the principles govern-ing
existence, the material universe, and the perception ofphysical
phenomena, as well as to analyze human behaviors.
God speaks through these forms. Virgin nature was therst book,
which made the Truth visible. From the bosomof nature, man seeks to
transcend nature and nature herselfcan be an aid in this process,
provided man can learn tocontemplate her, not as an independent
domain of realitybut as a mirror reecting a higher reality, a vast
panoramaof symbols which speaks to man and has meaning for
L.M. Dabbour386Figure 9 Proportions of the Venus and the Earths
meanorbits are based on the sacred mean (Martineau, 2001).
Figure 10 Proportions of the Mercurys and the Earths mGeometric
proportions are used by Muslim designers as themost valuable tool
of design process to produce orderedpatterns that govern esthetic
beauty in designed spaces,surfaces and objects. They present us the
Principles ofNature in their own language. By applying the golden
mean(Phi) and the root proportions, geometric patterns areproduced
to be applied to the elds of building crafts, suchas tiles, mosaic,
plaster and wood, as well as to the eld ofbook art.
By diminishing the polygon contained in the circle ofUnity
toward the center until the stars, which control theshape of the
pattern, appear, the Muslim artists preservethe esthetics of these
proportions and grant them exquisitebeauty at a higher level than
direct, material expression.
The system of geometric design starts from the circle (thebasic
unit), from which the pattern starts to unfold,creating harmonious
divisions of the circle in four stages:
1) The planning stage: starting by determining the propor-tional
systems based on the unit pattern structure withinthe circle of
Unity. The decision is based on the symbolicmeanings underlying the
geometric pattern and itsrelation to micromacro cosmos.
2) The division phase: construction of the basic
3) Pattern order and structure: initiating the crossing linesto
create the artistic shape of the pattern on naturaljunctions formed
by those lines. This gives rise to a series
n orbits are based on the sacred mean (Martineau,
Geometric proportions as a tool of design:dy modelwhnoportional
roots govern the proportion of our world,ich can be found in the
proportions of all living andareproGeometry is the very basis of
our reality. Therefore, wee in a coherent world governed by
underlying laws. Theyalways manifested in our world. The golden
of points that can be used in the development of patterns.This
type of framework forms the driving geometry forthe relatively
simple Islamic patterns with which we arefamiliar.
4) Desired pattern revealing: establishing the
geometricvariations of the pattern and dening its boarder lines.It
is derived from all the vital proportion systems basedon a single
unit. The process can be repeated inde-nitely, presenting the same
center everywhere andnowhere. It is ratio, rather than measurement,
thatdetermines the relative lengths of crucial dimensions.
The innitely repeating geometrical patterns and therules of
geometric construction are a reection of theunchanging laws of God.
They are based on estheticproportions as seen in the rhythm of the
Creation and canbe presented according to the design process in the
follow-ing study models.
4.1. Fourfold to eightfold pattern
space, is a symbol of the divine throne and its
applicationwithin architecture is reected in a Moroccan ceramic
(Zilij)panel and in the harmonic diminishing of the eight-fold
starin the Alhambra Palace, The Hall of The Abencerrajes, andthe
Hall of the Two Sisters (Figure 13).
4.2. Fivefold to tenfold pattern
This part of geometric study shows a construction of
thegeometric panel based on proportional geometry. Itsesthetic
advantage is related to the golden section, showingone of the many
ways to apply the geometry to formdifferent patterns using a
variety of materials.
Figures 14 and 15 show the construction systems of a
ve-to-tenfold pattern which appears on the body of Salah
Al-Dinwooden Minbar (Pulpit) at Al-Aqsa mosque (Jerusalem), on
awooden door from Mumluk period (Cairo) and on a frontispieceat a
Mamluk Quran. Ten pointed geometry lends itself to a widevariety of
design possibilities through relatively small variationsin the
underlying relationships and to the creation of different
The complexity is introduced on a relatively simple basis by
in thn noatterns
Geometric proportions 387Figure 11 Construction stThe two
simplest geometric constructions which form thebasis for many of
the patterns to be found in Islamicdecorations are the
constructions of four and eight pointedgeometries respectively.
These relatively simple geometri-cal constructions are easy to
develop by connecting variousintersections, forming the basis for a
variety of patternmaking.
Figure 11 shows how this kind of geometric patterns developswhen
they are added together following the basic rules createdby the
selection process. By illustrating how small changes canaffect the
overall pattern according to the types of pattern andhow they are
achieved by simple changes, it is possible to seehow a very small
differentiation can produce a dramaticallydifferent overall
Figure 12 illustrates the construction of eight pointedgeometry
based on subdividing the square and O2 rectan-gles. The octagon,
associated with the eight directions of
Changing intersectiodifferent pconstructio
Stage 1The planning stage
Stage 2The division phases of four pointed patterns.applying
colors and doubling of the structure lines while
e selected des creates n
Stage 3Order and structure
Stage 4Pattern revealingpatterns at different scales as a unied
4.3. Sixfold to twelvefold pattern
Twelve pointed geometry can be constructed from sixpointed
geometry. The hexagon is one of the most impor-tant forms in
Islamic geometry. It is simple to construct, ithas the capability
of producing, by means of repetition, anoverall coverage of a
surface, it contains the importantrelationship of O3 proportions,
and it bears a strongsimilarity to the circle, a symbol of the
Creation in Islam.
Figure 16 is a study based on variations of the panelsof ceramic
tile. Their underlying geometry is based on therelationships
between the circles containing the 612 pointedgeometry, which is
derived from the central six-pointed roseand a combination of a
square, a lozenge and a triangle.
L.M. Dabbour388Stage 1The planning stage
Stage 2 The division phaemploying the technique of cutting the
tiles in such a way as toimply the interweaving of the running
The pattern is both logical and rhythmical, i.e.,
bothmathematical and melodious, which is the most
signicantcharacteristics of the spirit of Islam, showing its
balancingu-nity in multiplicity or multiplicity in unity within a
series ofregular geometrical gures contained within a circle, or a
seriesof regular polyhedral contained within a sphere
(Burkhardt,1986; Burckhardt, 1987).
Figure 12 Construction stage of eight poin
Figure 13 Applications of the octagon based on eight pointed
paeight will, that Day, bear the throne of thy Lord above them
(TheStage 4Pattern revealing
Stage 3 Order and structureFigure 17 shows how a relatively
simple pattern based on six-pointed geometry might be developed
into so many potentialchoices for the designer, which accounts for
the great numberof design variations that are possible.
It is surprising that how many variations can be madefrom a
simple geometric shape. Figure 18 illustratesa pattern based on a
study using six-fold geometry. Therst diagram illustrates the basic
construction, beginningwith the development from a circle. The
second one shows
ted patterns based on O2 proportions.
tterns in architecture And the angels will be on its sides,
andHoly Quran, Chapter 69, verse 17).
Geometric proportions 389Stage 1The planning stage
Stage 2The division phasethe six pointed divisions. It is these
selections shown in thethird diagram that create the possibility
for differentpatterns to evolve. The fourth is the result of this
drawingand selecting process.
Figure 14 Construction of a ve-to-tenfold pa
Figure 15 Applications of a ve-to-tenfold pat
Figure 16 A study of 6Stage 3Order and structure
Stage 4Pattern revealingThe Ikhwan Al-Safa (the Brothers of
Purity) stressed theimportant symbolism of number six, regarding
number 6 asa perfect number. The number 6 consists of 1 2 3; at
thesame time also 1+2+3. Any number with this quality is
ttern based on the golden mean proportion.
tern based on the golden mean proportion.
12 pointed patterns.
L.M. Dabbour390considered a perfect number. Also, it was on the
sixth dayof the Creation that God created man. There are six
directionsof space as well. The six-sided hexagon is therefore a
symbol ofthe universal man (Ardalan and Bakhtiar, 2000).
Figure 18 shows the signicant study on tile patterns andtheir
underlying geometry, particularly the visual strengthof the
geometric structure in the application of thesepatterns. The
construction of such natural geometries formsthe basis upon which
artisans on building sites set out theirdesigns and work.
Figure 17 Potential variations of 612 pointed patterns based
Figure 18 Analysis stages: example of s
Figure 19 Applications ofFigure 19 shows the applications of 612
pointed patternsbased on O3 proportions in a wooden panel and a
paperbased geometric stars (medallion).
These studies illustrate only a small number of
numerouspossibilities out of the variations of proportional
patternsbased on simple polygon geometries. The ways of alteringthe
relationship between the elements of these geometriesappear to be
relatively simple. However, every decisionresults in diversied
complex patterns that are quite diff-erent from each other.
the same structure as in Figure 16 based on O3 proportions.
tep by step unfolding of the pattern.
612 pointed patterns
Islamic patterns, by their very nature, do not have anydirection
underlain in their geometry. Rather, they tend tobe formed in elds
with no apparent ending. The framing ofpatterns tends to be
controlled by proportion systems. Inother words, it is an
objectively intellectual qualitativegeometry, reecting Truth in
space. Ibn Khaldun states:Geometry enlightens the intellect and
sets ones mindright. All its proofs are very clear and orderly. It
Burckhardt, Titus, 1987. Mirror of the Intellect. State
University ofNew York Press, New York, USA, p. 219,227.
Burkhardt, Titus, 1986. Sacred Art in East and West: Its
Principlesand Methods. Perennial Books, Indiana, USA, p. 101.
Concise Oxford English Dictionary, 1999. Oxford University
Critchlow, Keith, 1976. Islamic Patterns: An Analytical and
Cosmo-logical Approach. Schocken Books, Thames and Hudson,
London,UK, p. 4,9.
Critchlow, Keith, 1987. Order in Space: A Design Source
Book.Thames and Hudson, USA, p. 9.
El-Said, Isasam, 2001. Islamic Art and Architecture: The Systems
Guenon, Rene, 1995. The Reign of Quantity and the Sign of
theTimes. Sophia Perennis, Ghent, p. 8,170.
Guenon, Rene, 1994. The Great Triad. South Asia Books, New
Geometric proportions 3915. Conclusion
We can conclude that proportion is a characteristic of
(tradi-tional) Islamic patterns, serving as a tool of self-guiding
processfor esthetically proven design. Muslim builders knew of
theautonomy or inner laws in constructing spaces and patterns.The
relations among various parts can be seen everywhere inancient
buildings. In other words, buildings were designed withparticular
care, exhibiting mastery in pattern design of theirspaces and
Geometric proportions regulate the order of patterns basedon
mathematical ratios, which is inuential in understandingthe
universe, man and nature; these proportions are, by theirnature,
the essential ingredients in sacred geometry, asPythagoreans stated
that these harmonic ratios render musicin a balanced pattern.
Geometric proportion is strongly linked to Islamic
cosmology,philosophy and metaphysical dimensions. It brings
meanings andspiritual exercises for the viewer, deconstructing the
meaningsunderpinning the geometric framework. As such, the viewer
ismore than an observer; he or she is a participant in
theestablishment of a strong link with geometry symbolizing
man,nature and cosmos.
The geometry as well as its rhythm shown in Islamic
patternsillustrates an innite variety, permitting and
encouragingcontemplative reections. It is one of the most powerful
formsof sacred art It is a source of contemplation that allows
ourminds to wander and contemplate the innite. These patternswere
developed with strict geometric rules, relating to theunderstanding
of natural forms based on geometric ratios in thecosmos, set as the
prime mover behind design.
Ardalan, Nader, Bakhtiar, Laleh, 2000. The Sense of Unity: The
SuTradition in Persian Architecture. Kazi Publications, p. 21.USA,
p. 23.Hambidge, Jay, 1920. The Elements of Dynamic Symmetry.
University Press, NewHaven, USA, p. 23.Hecht, Laurence, 1988.
Mysterium microcosmicum: the geometric
basis for the periodicity of the elements. 21st Century
Ibn, Khaldun, 1958. The Muqaddimah Franz Rosenthal.
PantheonBooks, New York, USA 378.
Lawlor, Robert, 1989. Sacred Geometry: Philosophy and
Practice.Thames and Hudson, New York, p. 3,48,82,92.
Lings, Martin, 1976. The Quranic Art of Calligraphy and
Illumina-tion. Tajir Trust, London, p. 13.
Martineau, John, 2001. A Little Book of Coincidence. Walker
andCompany, New York, U.S.A, p. 15,21.
Nasr, Sayyed Hussein, 1978. An Introduction to Islamic
CosmologicalDoctrines. Thames and Hudson, UK, p. 45.
Nasr, Seyyid Hossein, 1997. Man and Nature. ABC
InternationalGroup, Chicago, USA, p. 95.
Pennick, Nigel, 1994. Sacred GeometrySymbolism and Purpose
inReligious Structures. Capall Bann Publishing, San Francisco,
Rawles, Bruce, 1997. Sacred Geometry Design Sourcebook.
ElysianPublishing, Eagle Point, Oregon, p. 87.
Schneider, Michael, 1994. A Beginners Guide to Constructing
theUniverse: The Mathematical Archetypes of Nature, Art andScience.
Harper Collins, New York, p. 10.
Schuon, Frithjof, 2003. Survey of Metaphysics and Esoterism.
WorldWisdom, Indiana, USA, p. 48.
Schuon, Frithjof, 1984. The Transcendent Unity of Religions.
QuestBooks, USA, p. 62.
Singer, Lynette, 2008. The Minbar of Saladin: Reconstructing
aJewel of Islamic Art. Thames and Hudson, London, UK, p. 110.
Skinner, Stephen, 2009. Sacred Geometry: Deciphering the
Code.Sterling, New York, p. 7,91,107.
The Holy Quran. Chapter 95, verse 4 (95:4).error. (Ibn Khaldun,
1958) Geometric Design. Garnet Publishing Ltd., UK, p. 15.possible
for errors to enter into geometric reasoning,because it is well
arranged and orderly. Thus the mind thatconstantly applies itself
to geometry is unlikely to fall into
Geometric proportions: The underlying structure of design
process for Islamic geometric patternsIntroductionGeometric
proportional systemsGeometry in man, nature, and
Geometric proportions as a tool of design: study modelFourfold
to eightfold patternFivefold to tenfold patternSixfold to