Teachers' resource: Maths and Islamic art & design

Tiles, 13th-14th century, Museum no. 1074-1875. © Victoria & Albert Museum, London

Tiles, fritware with lustre decoration, Kashan, Iran, 13th-14th century, Museum no. 1074-1875. © Victoria & Albert Museum, London

This resource provides a variety of information and activities that teachers may like to use with their students to explore the Islamic Middle East collections at the V&A. It can be used to support learning in Maths and Art. Included in this resource are sections on:

  • Principles of Islamic art and design 
  • Pre-visit activities
  • Activities to do in the museum
  • Activities to do back at school

Islamic art explores the geometric systems that depend upon the regular division of the circle and the study of Islamic art increases appreciation and understanding of geometry. The use of these geometric systems creates a harmony among Islamic decorative arts and architecture, which is consistent with the Islamic belief that all creation is harmoniously interrelated.

Approaching an abstract subject in a concrete way provides a means of extending maths into other curriculum areas. The context of the Museum expands and enriches students' appreciation of the application of geometry in a cultural context and develops the sense of different cultural identities. Students have the opportunity to become familiar with the relationship between geometry and design and this can give confidence to students who have never seen themselves as 'good at art'.

Islamic Middle East (Room 42) and South Asia (Room 41) are referred to in the Museum activities. This resource also suggests activities for students to carry out before and after they visit the Museum.

National curriculum links

The activities based on geometric Islamic patterns in this booklet support learning about shapes, space and measures. Students at Key Stage 1 and 2 can learn to recognise circles, triangles, squares and hexagons, and to create pictures using 2-D shapes. They learn to identify lines of symmetry and to recognise reflective and rotational symmetry. Students at Key Stage 2 and 3 can study transformational and symmetrical patterns to produce tessellations. The activities are particularly useful for cross-curricular links with Art and Technology projects.

Preparation for a visit

We strongly suggest that teachers make a preliminary visit to the V&A and undertake the activities themselves before introducing these to students. Students will need to construct patterns for themselves in order to develop an understanding of how the shapes relate to each other. Allow plenty of time for these activities. Some students may lack the co-ordination required to manipulate a compass. Circular templates with the circumference divided into six or eight equal parts will help to get these students started.

We have provided a triangular grid for producing patterns with triangles and hexagons. We have also provided patterns that can be used to make card templates of the main shapes.

Download triangle grid template (PDF file, 60.4 KB)

Download circular template (PDF file, 116.7 KB)

Download octagon template (PDF file, 43.5 KB)

Download hexagon and triangle template (PDF file, 93.2 KB)

Panel of hexagonal tiles, 1550-1600, Museum numbers 908A to F-1894. © Victoria & Albert Museum, London

Panel of hexagonal tiles, fritware painted and glazed, Turkey or Syria, 1550-1600, Museum numbers 908A to F-1894. © Victoria & Albert Museum, London

Principles of Islamic art & design


Islamic faith
Islamic faith is based on the Islamic holy book, the Qur'an (sometimes spelt Koran), which followers of Islam believe to be the word of God as revealed through the Archangel Gabriel to the Prophet Mohammed in the early 7th century. The Prophet was born in Arabia in about AD 571 and died in AD 632. By the early eighth century Islam had spread by military conquest westward as far as Spain and eastward to Samarqand and the Indus Valley. Islam continued to expand, into Turkey and deeper into the Indian subcontinent, into north-western China and South-East Asia. Followers of Islam are called Muslims.

Art and design
The Islamic faith provides laws to govern both religious observance and social behaviour. While the Qur'an contains no specific prohibition on figural imagery, most interpretations of Islamic law have tended to discourage such imagery as potentially idolatrous, and figural elements such as pictures are rigorously excluded from most religious settings. However, there is a continuous tradition of using figures as part of decorative schemes in non-religious contexts, particularly in the illustration of books.

Islamic decoration consists of three main elements, which are often combined in the decorative scheme on a single object:

  • calligraphy in various forms of Arabic script (Arabic is the language of the Qur'an and therefore of God, and has a special significance in Islamic culture)
  • arabesques, scrollwork and other floral or plant-like designs
  • geometrical designs using a limited number of geometric shapes in many different ways

Geometry in Islamic design
The use of geometry is important in the development of Islamic ornament, whatever form it takes. Circles, for example, are crucial in designing arabesque patterns, and even calligraphy has been described as 'spiritual geometry.' The use of purely geometric elements to create elaborate patterns, though, has become a sophisticated form of decoration on its own. The appeal of Islamic geometric decoration lies in its logical interrelation of parts, reflecting in abstract form the underlying order found in nature.

Among the most important aspects of Islamic geometric design are repetition and variation. A series of tiles, for example, may consist of only one or two shapes but the patterns of the tiles may all be different. In other designs, a few different shapes may be combined to create a complex interlocking pattern.

Symmetry plays a part in most Islamic patterns. There may be a single line of reflective symmetry, usually from the top to the bottom, or there may be three or four lines of symmetry. Straight (translation) and turning (rotational) movements are also used. Sometimes reflective symmetry and the two kinds of movement are found in the same design. Symmetry and repetition give unity to the more complex designs, as in this panel with a pattern based on pentagons.

Circular tray of al-Nasir Nuhammad, 14th century, Museum no. 420-1854. © Victoria & Albert Museum, London

Circular tray of al-Nasir Nuhammad, brass inlaid with silver and gold, Egypt or Syria, 14th century, Museum no. 420-1854. © Victoria & Albert Museum, London

Pre-visit activities

Most of the patterns that your students will see in the Islamic objects at the V&A are based on the equilateral triangle and the square. Both can be made by using only a compass and a straightedge, and both can fit within a circle so that all points touch the circumference. Patterns based on equilateral triangles and hexagons are easy to make using a compass and straightedge because the radius of a circle divides its circumference into six equal parts.

When working with a compass it is a good idea to place a piece of thin card under the piece of paper on which you are drawing as this will help to stop the compass point from slipping. The pencil leg should always be a little longer than the stationary leg and the weight of your hand should be over the point to keep it in position and upright.

Triangles and hexagons

Open the compass about two inches and press the point into the paper. This is the 'invisible' starting point from which the design will unfold. Draw a circle with the compass.

Put the compass point anywhere on the circumference of the circle and swing the pencil leg so that a mark is made on the circumference. Move the point of the compass to the pencil mark and make another pencil mark on the circumference. Continue doing this round the circle until there are six marks. From these six marks the series of hexagons and six-pointed stars illustrated here can be made.

Drawing stars within a hexagon

Drawing stars within a hexagon

  1. Join up the points in sequence round the circle to make the six-sided polygon, a hexagon. This has three pairs of parallel lines
  2. Next join up every second point. You now have an equilateral triangle
  3. Join up the other three points and you have a second equilateral triangle. Together these two triangles make up a star. One triangle points up to heaven, the other points down to earth. Three pairs of parallel lines make up the star. In the middle of the star is another hexagon
  4. Joining up every second point of the inner hexagon, makes another equilateral triangle in the inner hexagon. Joining up the other points makes a second equilateral triangle and another six-pointed star with a hexagon in the middle
  5. This pattern can go on and on. In this sequence of patterns the stars and hexagons change position

In another sequence the points are always in the same position.

Six-pointed stars within a hexagon

Six-pointed stars within a hexagon

This is done by joining up the centres of the lines of the hexagons to make the triangles. To find the centres, lightly draw lines joining the opposite points of the star.

These lines will cross the sides of the inner hexagon in the middle.You can now join up the centres of every second line to make one equilateral triangle and the centres of the other three lines to make a star.

Download triangle grid template (PDF file, 60.4 KB)

The triangular or isometric grid template can be used to make patterns of hexagons and six-pointed stars. We suggest you tape a clean sheet of paper over the grid and draw on the plain paper using the grid as a guide. This has the advantage of allowing the pattern to develop without the grid becoming too much of a distraction.

Patterns on an isometric grid

Patterns on isometric grid

Point out to students that the grid can be used either horizontally or vertically depending on the pattern you are making. Ready-printed isometric paper is available from educational suppliers.

For a simple design start by colouring a small hexagon made up of six triangles. A triangle added to each of the sides of the hexagon will then make a six-pointed star. The star can be enclosed in a bigger hexagon by adding six diamonds. A bigger star and a bigger hexagon can then be made and so on.

Squares and octagons

The eight-pointed star which is made of two overlapping squares in a circle, is the basis of many Islamic patterns (1 & 2).

Squares and octagons

Squares and octagons

Notice the four pairs of parallel lines that make up the eight-pointed star. Joining up the points will make an octagon. In the centre of the eight-pointed star is another octagon (3).

The points of the eight-pointed star are short. In some designs, the sides of the squares in both directions are extended to create eight larger points (4).

Other designs are constructed by making a cross from the eight-pointed star. In many patterns, this cross is combined with the short-pointed eight-pointed star (5).

Download circular template (PDF file, 116.0 KB)

Make circular templates with the circumference divided into eight equal parts. Show students how to use these circle templates to make the octagon, the short-pointed eight-pointed star and the cross.

Another way to form a template is to fold a square of paper in half from corner to corner to form a triangle, fold this triangle in half and then in half again. Open it out, put your compass point in the centre where the fold lines cross and draw a circle. The fold lines will divide the circumference of the circle into eight. Join these points to make an octagon.

Shape recognition and shape groups

Students will need to have a good shape vocabulary and be adept at recognising shapes (circle, triangle, square, hexagon, octagon, six-pointed star, eight-pointed star, and regular and irregular polygons) to get the most from their visit to the Museum. Practice by doing some shape recognition exercises. Provide students with large-scale triangular grid paper, or use a triangular template, and ask them to cut out mosaic pieces and arrange them to form specific patterns. Create stars and other shapes using drinking straws.

Students also need to understand the relationship between groups of shapes: those based on three and six divisions of a circle are equilateral triangles; hexagons and six-pointed stars and those based on four and eight divisions of a circle are squares, octagons and eight-pointed stars. These groupings will determine how shapes fit together and which grids are used for making patterns.

In the Museum

Before coming to the Museum, make sure you have prepared and brought with you; copies of the triangular grid paper templates, some plain paper and coloured pencils (but not felt pens, they are not allowed in the Museum).

If you plan to do the activity in the Islamic Middle East gallery (room 42) based on the minbar you should take ready-cut octagon, octagonal stars and irregular hexagon shapes.

Download triangle grid template (PDF file, 60.4 KB)

Download octagon template (PDF file, 43.5 KB)

Download hexagon and triangle template (PDF file, 93.2 KB)

Download circular template (PDF file, 116.0 KB) This template also contains stars and crosses.

Drawing shapes and patterns from screens

Take students to the raised area in the centre of the South Asian room (Room 41). Look at the sandstone and marble screens. These are used instead of glass windows in India because they let in light and air but not too much sun and heat.

Some of the patterns are simple and some are very complex. They are not easy for primary students to draw so it may be better to start by asking questions that will help them to see how patterns are made.

Which screens have star patterns? Which have hexagons? How many different triangles can they see?

Ask students to choose their favourite screen and record the names of the shapes they recognise. Are there any irregular shapes? If so, draw one.

The screens shown here could be drawn using templates.

For Screen 1 you need the hexagon and a triangle template.

For Screen 2 you need the octagon template with each side divided into three.

Screen 1

Screen 1

Screen 3

Screen 3

Screen 2

Screen 2


Some students might like to try drawing designs directly on to their grid paper using coloured pencils.

They might start with the pattern based on stars and hexagons.

Conclude your work on the screens (like Screen 3) by asking your students to look in detail at all the other screens and find how many have hexagons, squares, triangles or octagons in their designs. Ask students to investigate whether there is a rule about which shapes go together.

When your students have finished drawing ask them to look around the room and find other geometric designs on textiles and objects and see if they are based on six or eight. Discuss the patterns your students find. If you intend to produce related artwork back at school, ask students to record the most commonly used colours.

Drawing tessellations and symmetry from objects

Start by doing some basic shape recognition in the Islamic Middle East gallery (Room 42). Ask students to find the three objects below:

Bowl with a geometric design; glazed earthenware; Iraq (probably Basra), 9th century. Museum no. C.1447-1924. © Victoria & Albert Museum, London
Bowl with a geometric design; glazed earthenware; Iraq (probably Basra), 9th century. Museum no. C.1447-1924. © Victoria & Albert Museum, London
Casket, wood with a mosaic veneer of mother-of-pearl, metal and stained ivory with verses in ivory marquetry; Iran (probably Tehran), 1800-50. Museum no. 501-1874. © Victoria & Albert Museum, London
Casket, wood with a mosaic veneer of mother-of-pearl, metal and stained ivory with verses in ivory marquetry; Iran (probably Tehran), 1800-50. Museum no. 501-1874.© Victoria & Albert Museum, London
Carpet fragment; wool warps, wefts and pile; Egypt (probably Cairo), 1468-96. Museum no. 150-1908. © Victoria & Albert Museum, London
Carpet fragment; wool warps, wefts and pile; Egypt (probably Cairo), 1468-96. Museum no. 150-1908. © Victoria & Albert Museum, London
Whiteware dish with a simple geometric design, about 850, Museum no. C.45-1952. © Victoria & Albert Museum, London

Whiteware dish with a simple geometric design, earthenware with lustre painted over an opaque glaze, Iraq (probably Basra), about 850, Museum no. C.45-1952. © Victoria & Albert Museum, London



Panel of star and cross tiles, 1262, Museum no. 1837-1876

Panel of 15 star and cross tiles from the shrine of Imamzadeh Yahya in Varamin (south of Tehran), fritware with lustre decoration, made by the potter Ali ibn Muhammad ibn Abi Tahir in Kashan, Iran, 1262, Museum no. 1837-1876. © Victoria & Albert Museum, London


Side panel of a minbar made for the mosque of Ibn Tulun, Egypt (Cairo), 1296, Museum no. 891-1884. © Victoria & Albert Museum, London

Side panel of a minbar made for the mosque of Ibn Tulun, Egypt (Cairo), 1296, Museum no. 891-1884. © Victoria & Albert Museum, London

Check that students can distinguish between the shape of the object and the pattern drawn on it. Ask your students to choose two or three patterns they like and sketch them. They could use the grid paper if it helps or draw round templates. Notice that some of the objects have different designs on each part. Students could sketch these individual designs too.

Tessellations
Ask students to find and record an example of a regular tessellation based on repeating one shape only (say, a hexagon) and an example of a semi-regular tessellation where two different shapes are fitted together and repeated (say, stars and diamonds). Discuss the use of tiles today. Why do we use square and hexagonal shapes and not pentagons?

Symmetry
Ask your students to look for the lines of symmetry in individual designs. Can they record a design with one line of symmetry and another with two or more? Which designs do not have a line of symmetry?

Students should look around the gallery to find patterns that use the triangle, hexagon, star, square, or octagon and try sketching some of the simpler patterns.

Students can use their star and cross template to make the tile pattern and can then draw in the different surface patterns.

More complex geometric shapes
The geometrical designs from Mamluk Egypt are some of the most complex in the gallery. Show your students the large wooden panel that originally formed part of the side of a minbar (pulpit) in the mosque of Ibn Tulun in Cairo.

A Mamluk officer named Lajin hid from his enemies in the abandoned and ruined Ibn Tulun mosque after the assassination of the reigning sultan. He vowed he would restore the mosque if he ever came to power himself. When he became sultan in 1296, he fulfilled his promise. The minbar from which this panel is taken formed part of the restoration.

Ask your students to find the octagons and eight-pointed stars in the panel. There are eight-pointed stars with short points that have been extended to form similar stars with long points. Prior to the visit prepare some ready-cut octagons, stars and irregular hexagons.

Working in small groups in front of the panel, ask students to lay the pieces out on coloured paper to recreate the pattern.

The missing shapes will be created in the spaces between your pieces. You could use gummed paper or double-sided cellotape so that the finished results can be stuck down.

A complete minbar from the end of the 15th century, also from Cairo, is behind you and to the left as you look at the panel in the gallery. Go on to look at the design on it. The main motif is a star whose points radiate outward to form a wheel-like pattern.

Look for the way this motif is repeated in varying sizes. Compare this design with the design on the panel from the mosque of Ibn Tulun. What similarities and differences are there? Find and draw examples of four-, five- and six- (or more) sided shapes.

Finally, show your students the wooden panel in the 'Geometry' display on the east wall of the gallery. This panel was part of a box-like structure marking the tomb of a holy man named Sayf al-Din Bakharzi in the city of Bukhara, in what is now the country of Uzbekistan.

The panel, made of carved wood with painted highlights, is rectangular in shape and features several distinct patterns. The main section contains a pattern made up of six-pointed stars and twelve-sided figures.

Below it another section has a pattern based on hexagons. The sides and top of the panel, on the other hand, have a border of motifs based on eight-pointed stars.

Before leaving the gallery discuss with your students what they have seen, which patterns they liked and why they liked them.

Minbar made for Sultan Qa'itbay, 1468-96, Museum no. 1050-1869. © Victoria & Albert Museum, London

Minbar made for Sultan Qa'itbay, wood with inlay of ivory, Egypt (Cairo), 1468-96, Museum no. 1050-1869. © Victoria & Albert Museum, London

Panel from a tomb-marker, 1300-1400, Museum no. 1437-1902. © Victoria & Albert Museum, London

Panel from a tomb-marker, carved wood with painted and gilded highlights, Uzbekistan (Bukhara), 1300-1400, Museum no. 1437-1902. © Victoria & Albert Museum, London

Back at school

Tile panel, about 1360, Museum no. 1978-1899

Tile panel from the tomb of Buyan Quli Khan, fritware with carved decoration and coloured glazes, Fathabad near Bukhara, about 1360, Museum no. 1978-1899. © Victoria & Albert Museum, London

A valuable follow-up activity is for students to reproduce some of the tile shapes they have seen. If everyone works to the same scale then the finished results can be sorted into shapes based on six and eight and displayed together in tessellating panels.

Ask your students to make drawings in colour of some of the objects and screens they have sketched at the Museum. Put the drawings up in the classroom so students can see each other's work. Compare and discuss the different patterns. Notice how they are made and whether they are based on six or eight.

Using the work they did in the Museum for inspiration, ask your students to develop designs of their own using the triangular grid as a guide. They could choose part of the design or the whole design to be a repeat pattern. By drawing over the design several times, or using a photocopier, students can see what type of pattern the repeat design makes. Ask them to use some of the colours they recorded in the Museum.

The work could lead into other kinds of artwork. Create card rubbings and mobiles based on the designs seen
in the Museum. Fabric printing could be based on tile designs. Hexagons and triangles could form the base for a patchwork. For a Technology exercise, moulds or forms could be designed to make tiles of different shapes.

If you have access to a computer, try making patterns based on hexagons, octagons and stars by manipulating the basic shapes in different ways.

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