The Art of Mathematics
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 westward by military conquest 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. As is often the case with constraints of one kind or another, this restriction has led Islamic artists to become masters of abstract geometric patterns, tilings and calligraphy.
Geometry in Islamic design
A common feature of Islamic art is the covering of surfaces with geometric patterns. This use of geometry is thought to reflect the language of the universe and help the believer to reflect on life and the greatness of creation. 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. Geometry is seen to be spiritual because circles have no end, they are infinite and so they remind Muslims that Allah is infinite. Complex geometric designs create the impression of unending repetition, and this also helps a person get an idea of the infinite nature of Allah. The repeating patterns also demonstrate that in the small you can find the infinite, a single element of the pattern implies the infinite total.
Symmetry also 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 these, as well as reflective symmetry, are found in the same design.
National Curriculum links
The following activities based on geometric Islamic patterns support learning about shapes, space and measures. Pupils in Key Stage 1 and 2 can learn to recognise circles, triangles, squares and hexagons, and to create pictures using 2D shapes. They learn to identify lines of symmetry and to recognise reflective and rotational symmetry. Extension activities for more able pupils could include the study of transformational and symmetrical patterns to produce tessellations.
These activities will address the learning objectives in the Primary Framework Understanding Shape strand, particularly those for Year 5 and Year 6.
You will need a selection of Islamic patterns which you can find easily on websites on the internet or Google images.
Examine and discuss a range of Islamic patterns. What shapes can the children see? What are the properties of these shapes? Through these activities, the pupils will be able to discuss shape vocabulary in relation to circle, triangle, square, hexagon, and octagon.
Give children a range of 2D shapes (those you get from published materials) and ask them to fit them together so there are no gaps. After some time, ask the children which ones fit together and which ones don’t. (Oblongs, rhombus, parallelograms, equilateral triangles, squares and hexagons will tessellate.) Once the children have had an opportunity to explore, ask them to draw a pattern by fitting their shapes together and drawing around them. This could be developed by asking the children to colour in, using a repeating pattern and explaining how they did it.
Examine and discuss a range of Islamic patterns. What shapes can the children see? What are the properties of these shapes? Through these activities, the pupils will be able to discuss shape vocabulary in relation to regular and irregular polygons. Ask the children to look for the lines of symmetry in individual designs. Can they see a design with one line of symmetry and another with two or more? Which designs do not have a line of symmetry? In a design, identify a shape and demonstrate how this can be tessellated. If using an Interactive Whiteboard you could draw around the shape then translate or rotate it to show how it would tessellate. You could extend more able pupils by asking them to identify an example of a semi-regular tessellation where two different shapes are fitted together and repeated. Why do some shapes tessellate and others do not?
Most of the patterns that your pupils will see in Islamic artwork are based on the equilateral triangle, square, hexagon and octagon.
Squares and octagons
An eight-pointed star forms the basis of many Islamic patterns. This can be made by overlapping two squares.
Discuss the properties of the square. Ensure that pupils know that a square rotated about the centre of rotation is still a square!
Ask pupils to draw a square using a ruler.
Next ask them to rotate the paper by 45˚ or 1/8th of a turn and draw a second square directly over the first square. You could draw links between compass points.
For pupils that need extra help, provide a square template to draw round and then rotate 1/8 of a turn or 45˚. What do the pupils notice about the shape in the centre of the eight-pointed star?
Triangles and hexagons
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.
Ask the pupils to draw a circle with the compass. Then ask them 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 can be made – see the illustrations below.
- Join up the points in sequence round the circle to make the six-sided polygon into a hexagon. Ask the children to discuss the properties of the shape e.g. Is the shape regular/irregular? How many parallel sides? How many angles? Ask the children to measure the internal angles using an angle measurer, what do they notice?
- Next pupils will need to join up every second point – they will now have an equilateral triangle. Ask pupils what shape they have now? How could they provide evidence to support their argument?
- Then they must join up the other three points of the hexagon to make 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.
- 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.
- This pattern can go on and on. In this sequence of patterns, the stars and hexagons change position. Ask pupils to discuss the relationship between triangles and hexagons.
You can find the source of this resource on the V & A website.
Health and Safety
When working with a compass it is a good idea to ask the children 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.
Links with ICT
Ask pupils to try to make patterns based on hexagons, octagons and stars by manipulating the basic shapes in different ways.
You could ask the children to reproduce this image using Logo. More ideas like this are available from the Nrich website.
Page header - Islamic tile photograph by Effervescing Elephant some rights reserved
Geometry in Islamic design tile photograph by Chris Applegate some rights reserved