Teachers' Resource_ Maths and Islamic Art & Design

3/18/2014 Teachers' resource: Maths and Islamic art & design - Victoria and Albert Museum

http://www.vam.ac.uk/content/articles/t/teachers-resource-maths-and-islamic-art-and-design/ 1/8

Tiles, fritware with lustre decoration, Kashan, Iran, 13th-14th

century, Museum no. 1074-1875. © Victoria & Albert Museum,

London

Teachers' resource: Maths and Islamic art & designThis 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

(http://www.vam.ac.uk/__data/assets/pdf_file/0008/179459/islamic_triangular_grid_template.pdf)

(PDF file, 60.4 KB)

Download circular template

(http://www.vam.ac.uk/__data/assets/pdf_file/0005/179456/islamic_circular_grid_template.pdf)

(PDF file, 116.7 KB)

Download octagon template

(http://www.vam.ac.uk/__data/assets/pdf_file/0007/179458/islamic_octagon_grid_template.pdf)

(PDF file, 43.5 KB)

Download hexagon and triangle template

(http://www.vam.ac.uk/__data/assets/pdf_file/0006/179457/islamic_hexagon_and_triangle_template.pdf)

(PDF file, 93.2 KB)

Principles of Islamic art & design

http://www.vam.ac.uk/__data/assets/pdf_file/0008/179459/islamic_triangular_grid_template.pdf

http://www.vam.ac.uk/__data/assets/pdf_file/0005/179456/islamic_circular_grid_template.pdf

http://www.vam.ac.uk/__data/assets/pdf_file/0007/179458/islamic_octagon_grid_template.pdf

http://www.vam.ac.uk/__data/assets/pdf_file/0006/179457/islamic_hexagon_and_triangle_template.pdf



Panel of hexagonal tiles, fritware painted and glazed, Turkey or

Syria, 1550-1600, Museum numbers 908A to F-1894. © 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

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.

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.



Drawing stars within a hexagon

Six-pointed stars within a hexagon

Patterns on isometric grid

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.

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.

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.



(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.

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).

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).




Squares and octagons



(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.



(PDF file, 60.4 KB)

Download octagon template

(http://www.vam.ac.uk/__data/assets/pdf_file/0007/179458/islamic_octagon_grid_template.pdf)

(PDF file, 43.5 KB)

Download hexagon and triangle template

(http://www.vam.ac.uk/__data/assets/pdf_file/0006/179457/islamic_hexagon_and_triangle_template.pdf)

(PDF file, 93.2 KB)



(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.



http://www.vam.ac.uk/__data/assets/pdf_file/0007/179458/islamic_octagon_grid_template.pdf

http://www.vam.ac.uk/__data/assets/pdf_file/0006/179457/islamic_hexagon_and_triangle_template.pdf




Screen 1 Screen 3Screen 2

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

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, earthenware

with lustre painted over an opaque glaze, Iraq (probably

Basra), about 850, Museum no. C.45-1952. © Victoria & Albert

Museum, London

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:

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.

http://www.vam.ac.uk/__data/assets/image/0010/198892/27008-large.jpg





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

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.



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

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, carved wood with painted and

gilded highlights, Uzbekistan (Bukhara), 1300-1400, Museum

no. 1437-1902. © Victoria & Albert Museum, London

Back at school

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.




Documents

Teachers' Resource_ Maths and Islamic Art & Design