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The Prince’s School of Traditional ArtsIn partnership with Al-Turath Foundation

Design Principles Workshop

Study GuideProportional Systems in

Islamic Architecture

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PSTA Workshops with Al-Turath Foundation

UNDERSTANDING THE LANGUAGE OF THE BUILDING ARTS IN THE CONTEXT OF

RIYADH’S BUILT HERITAGE2007

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UNDERSTANDING THE LANGUAGE OF THE BUILDING ARTSIN THE CONTEXT OF RIYADH’S BUILT HERITAGE

Nature provides many examples of absolute beauty which can only serve to inspire the architect & craftsman-artist alike. Nature’s beauty consists of the beautiful interaction between straight and curved, crystalline and biomorphic. There is infinite variety in her essential unity.

This two-week workshop explores the geometry found in nature and in Islamic architecture and adornment. The symmetries which produce the crisp lines of a geometric pattern often lie hidden behind the organic curves and growth patterns of plants and creatures. Participants in this workshop will learn to construct root proportional systems using compasses and ruler and to compose the designs for architectural elements using the knowledge of order and symmetry they have acquired. Participants will also explore some elements of colour harmony as they relate to nature.

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DESIGN PROJECT

The project is to observe and understand the technical construction of proportional rectangles and their application in the design of a complete architectural elevation and detailed section, such as decorated door or window, with surround (this may also include the use of arches, as appropriate). By referring to the outline drawings of Root Two, Root Three and Golden proportional rectangles, the objective is to make designs using studies of geometric motifs and compositions. The drawings and tracings of geometric elements are inserted into predetermined layouts using temporary fixings so that a range of designs for compositions can be made by experimentation, which are photographed as each composition is tried out. By process of making and remaking a series of designs emerge to be reviewed and discussed amongst staff and students. Each student will select drawings to be finished using rendering techniques to express qualities of light & dark, materials and substance of structure. The eventual result of this workshop will be selected designs to be mounted for a small exhibition to support the professional activities of future architects and designers

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ROOT THREE PROPORTIONS in the design of architectural elements

Figs a,b,c & d examples of architectural composition and details In Saudi Arabia that approximate to Root Three proportions

a b d

c

Analysis of Root Three proportions within the tree-fold and six-fold divisions of the circle

DESIGN PROJECTThe project is to observe and understand the technical construction of proportional rectangles and their application in the design of a complete architectural elevation and detailed section, such as decorated door or window, with surround.

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Figs a,b,c examples of architectural composition and details In Saudi Arabia that approximate to Root Two proportions

ROOT TWO PROPORTIONS in the design of architectural elements

a

b c

The analysis of elevation ‘c’using Root Two proportions

The Root Two rectangle

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Great Mosque and Redevelopment of the Old City Centre , Riyadh, Saudi, ArabiaArchitect: Rasem Badran, Amman, Jordan Client: Arriyadh Development Authority, Riyadh, Saudi Arabia

a b

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c

Figs a,b,c & d various views of the complex showing many opportunities for the application of proportional rectangles

The Great Mosque of Riyadh and the urban development of nearby public squares, gates, towers, parts of the old wall, streets, and commercial facilities, comprise the second phase of a master plan to revitalise the Qasr al Hokm district, the old centre of Riyadh. (The governorate complex, and the municipality and police headquarters were completed in the first phase.) For the new work, architect Rasem Badran has recreated and transformed the spatial character of the local Najdi architectural idiom without directly copying it. Externally, the complex is a group of buildings behind walls, punctuated by such traditional elements as gates and towers. Within, columns, courtyards and narrow passageways recall the traditional uses of space. The mosque, set within public areas, takes its traditional place as a centre of worship integrated into the urban fabric, rather than standing clear as an independent monument. Mosque components -- courtyards, arcades, and the flat-roofed prayer hall - are ordered and articulated in the traditional way. Two square minarets indicate the qibla direction on the skyline.

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The outer walls are clad in local limestone, penetrated by small, triangular openings in patterned formations, that resemble traditional building practices and create a further dialogue between the past and the present, while helping to cut the harsh glare of the sun. The courtyards and open squares are landscaped with palm trees to provide shade; granite benches and drinking fountains make them a popular place for families. The jury notes that because the mosque has already elicited interest in the intellectual community, its underlying design methodologies may affect for the better the design of future mosques.

Great Mosque and Redevelopment of the Old City Centre , Riyadh, Saudi, ArabiaArchitect: Rasem Badran, Amman, Jordan Client: Arriyadh Development Authority, Riyadh, Saudi Arabia

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One of the main elevations of the urban development in the Qasr Al-Hokm distict

The analysis of an example elevation based on the above using Root Two & Root Three proportions

DESIGN PROJECTThe project is to observe and understand the technical construction of proportional rectangles and their application in the design of a complete architectural elevation and detailed section, such as decorated door or window, with surround.

ROOT TWO

ROOT THREE

GOLDENMEAN

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THE PRACTICE OF GEOMETRY

Geometry is an orderly discipline consisting of laws governing the properties of point, line, plane, and solid. It is a science which has always been explored and practiced by mankind; each civilization has used geometry in some way. The classical Greeks are particularly well-known for the contributions of mathematicians such as Pythagoras and Euclid, but the principles they codified long preceded them. Islamic artisans have taken the basic principles presented by Euclid and transformed them into complex and sophisticated patterns and architectural forms which express their love of beauty and creation.

Ibn Khaldun recorded the transmission of the geometric arts and traditional science from the work of the ancient Greeks to the publication of translations by Islamic scholars. Euclid’s book The Elements was the first Greek work to be translated in Islamic civilization during the time of Abu Ja’far al Mansur and was entitled Kitab al-usul wa-l-arkan, ‘Book of Basic Principles and Pillars’, which was one of the seminial works in the renewal of traditional science in Islam (Ibn Khaldun The Maqaddimah, trans. Franz Rosenthal, Abridged N.J. Dawood [Routledge Kegan & Paul 1967], p. 378). Ibn Khaldun also mentions the Seven Liberal Arts studied in Plato’s Academy including Geometry, considered to be vitally important for the education of a student. “For geometry is the study of the eternally existent.” (Plato, Republic VII.527b).

The quest to study geometry begins with the appreciation of the fundamental figures of point, line and circle. The first touch of the pair of compasses or pencil upon the surface or ground on which the drawing is supported is the generation of a single point. From the point of origin, two modes of line are possible: the arc of a circle drawn with the aid of the pair of compassesand the straight line drawn using the square or ruler. By drawing overlapping circles and lines using just a pair of compasses and a straight edge, the student begins to explore the different symmetry groups within the generation of the basic polygon shapes.

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TOOLS OF TRADITIONAL GEOMETRY

The traditional compass with the ‘circle & dot’ hinge A Moroccan craftsman using the

North African Dabet

North African Dabet

The arts of geometry are governed by the significance of

the essential traditional tools used during the design process.

The compasses (or dividers) are thought in several traditions to

represent cosmic rhythms of the universe and the firmament of the heavens, while the square was thought to relate to earth

measure, geo – metry.To the ancient Greeks geometry

began in the culture of ancient Egypt with the reinstatement of

the fields after they were flooded by the Nile, however they thought of the elements of

geometry as being timeless.

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The point and the circle are closely related; the circle of the sun is itself a point which appears to circle the earth. Circular movement is a pattern nature returns to again and again.

POINT & CIRCLE

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Circles in nature echo the point at their centres. Overlapping circles generate lines.

POINT CIRCLE & LINE

15The sinuous movement of a sidewinder as it moves across the scalding sands of the desert produces a series of straight lines.

The point and line are essential elements for the progression into two dimensions and the later construction of polygon shapes, grids and patterns. Here we see the potentiality to understand the qualities of the ‘curved’ and the ‘straight’ tendencies that give rise both to crystalline and flowing forms, geometry and biomorphic motifs (arabesque – islimi). These are the two poles of Islamic architectural art & design.

POINT & LINE

A wooden door with lace patterns and decorated ‘nose’, Saudi Arabia.

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The overlapping of two circles generates a shape called the ‘vesica’. This shape is found in nature and is also used in traditional architectural adornment.

LINE & PLANE

Pond weed Potamogeton Colortus ‘Vesica’ motif on a Saudi door panelPlanctonic algae Diatom Planctonic algae Diatom

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The Palace of Sa’d dominating the ruins of Turayf with pierced motifs of triangular and square primary shapes that also result from the use of ‘adobe block’ the basic building material of the area.

The overlapping of two circles creates shapes which recalls the sun and moon as it moves through its phases. The overlapping, or vesica shape generates an equilateral triangle, the first polygon, the equilateral triangle.

PLANE

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THE CIRCLE DIVIDES ITSELF

Accuracy and precision of drawing becomes increasingly important to the geometer as the complexity of the patterns increases. If the point of the compass is not in the correct place, the circle cannot be drawn correctly. Assuming the artist is right-handed, greater accuracy can be achieved by using the left hand to carefully guide the point of the compass and ensure that it is precisely positioned.

The flowers of Allium christopii indicating six-fold symmetry

The traditional compass with dot & circle hinge

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Saudi wall design from Marat near Shaqra (Dir ‘iyyah)

THE EMERGENCE OF SHAPE

By keeping a fixed compass radius, it can be seen that a

circle’s circumference divides naturally into six,

such that six circles fit precisely around the central seventh circle. This motif is

frequently used as a decorative motif, as seen

here in the carved plaster and on the carved and painted wooden door.

Carved & painted door design from al-’Uthaibat Farm, Riyadh, Saudi Arabia

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THE TRIANGLE & THE CIRCLE’S SIMPLE DIVISION INTO SIXTHE BASIS OF ARCHITECTURAL ADORNMENT

A simple circular matrix forms the basis of this complex yet elegant pattern in carved stucco, Fes, Morocco

The Zaouia Fasouz Casbah, Morocco photograph by Andre Paccard

A carved and painted wooden window shutter, al-’Uthaibat Farm, Riyadh, Saudi Arabia

The first level of generation of the primary grid of triangles is a group of four, one surrounded by three the same, from within three overlapping circles drawn a radius width apart.

The primary grid of triangles continues to develop form the natural division of the original circle into six

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The triangle is the simplest polygon, followed by the four-sided square. There are several different ways to construct a square. One method is shown here.

Above, the cubic crystal of sodium chloride (salt) is the square expressed in three dimensions.

THE CONSTRUCTION OF THE SQUARE & FOUR-FOLD SYMMETRY

Dr Erwin Mueller’s micrograph of the tip of an extremely fine platinum needle (Ed Sir Bernard Lovell, The Physical Universe (Thames &Hudson), p.169

The original vesica almond shape (the decorative ‘qalb’element of Saudi doors) also gives rise to the construction of the square, dividing the radius into four. The primary square shape permeates the structure of the physical world , from atomic structure to the formation of minerals and the structure of plants on to man-made architectural buildings.

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The same geometry which is suggested by the unfolding of a lotus also yields the construction of the square, octagon and eight-pointed star

THE SQUARE - FOUR & EIGHT-FOLD SYMMETRY

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THE SQUARE - FOUR & EIGHT-FOLD SYMMETRY

Carved stucco, Ibn Tulun, Cairo, Egypt

Ceramic tile, Morocco

The proportions found within the basic square construction contain measurements for constructing many elaborate and beautiful patterns. Among other

things, this diagram shows how a large circle centred at each corner of the square can be used to draw an

octagon inscribed within the square abcd.

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THE GENERATION OF PRIMARY SHAPES FROM WITHIN THE ALL ENCOMPASSING CIRCLE AS THE BASIS OF ROOT PROPORTIONS

A. The construction of triangle, square & pentagon. B. Plane shapes divided from corner to centre. C. Unfolding similar triangles out from the centre D. Internal division of triangle, square & pentagon by circles of edge diameter. E Diminishing proportions by inscribing polygons & stars

A CB ED

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THE ROOT THREE PROPORTIONAL SYSTEM

The leaf pattern of Indian Balsam

The seed-pod of Asphodeline Lutea

The relationship of the root three rectangle to the hexagon & equilateral triangle

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THE ROOT THREE PROPORTIONAL SYSTEM

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THE ROOT THREE PROPORTIONAL SYSTEM IN ARCHITECTURAL DESIGN

A fountain decorated with ceramic cut tile Zillij, Fes, Morocco The panel of a mosque door, Istanbul, Turkey

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THE ROOT THREE PROPORTIONAL SYSTEM IN CONSTRUCTION OF AN ISLAMIC PATTERN

The specimen pattern within the root three rectangle The specimen pattern within the root three rectangle The pattern as a cut marble panel of the Itimad Ud-Daula

The subdivision of the root three rectangle by circles drawn with the radius equal to half of its short side drawn from the centre and corners of the rectangle is the basis of a classical Islamic pattern. The circumference of the circles is divided into twelve and four equilateral triangles are inscribed in each circle. This in turn gives rise to the generation of a variety of pattern shapes.

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THE ROOT THREE PROPORTIONAL SYSTEM IN THE ELEVATION OF THE TAJ MAHAL

The triangle is the simplest polygon and also gives rise to the root three proportional rectangle. This architectural drawing also shows the analysis of its elevation which is overlaid in red. It also demonstrates the coincidence between the root three rectangle and its subdivision with various horizontal levels in the architectural composition of the Taj Mahal.

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THE ROOT THREE PROPORTIONAL SYSTEM IN ARCHITECTURAL DESIGN

A carved wooden door and surround, Jeddah, Saudi ArabiaThe subdivision of the root three rectangle as possible door design compositions