Magazine article Mathematics Teaching

Engaging with an Islamic Pattern

Magazine article Mathematics Teaching

Engaging with an Islamic Pattern

Article excerpt

Ian Sugarman investigates using Turtle Tracks

I have had a long-time fascination for the geometric patterns that decorate mosques and palaces around the world. So imagine my pleasure to be given the book Islamic Geometric Patterns on a recent birthday. The author, Eric Broug, provides a detailed guide to the ways in which these amazing patterns were constructed using basic geometrical drawing instruments, compasses and ruler.

It's a pity that we seem to have abandoned this exercise in schools. Yet I do remember well being encouraged to investigate the drawing of patterns using circles and arcs, and a prize being awarded to the most impressive examples.

I believe the time is ripe to attempt to re-instate students' engagement with geometric patterns through the medium of software. In this article I want to illustrate a way that this can be done.

In his book, Broug classifies the patterns into Easy, Intermediate and Difficult. I chose one of the easy ones, a 14th century design taken from a building in Iran, the 'Abd-al-Samad Complex. Figure 1.

It then shows in detail how to construct the pattern just using pencil, paper, compasses and ruler. Figure 2

It is always valuable when first exposed to a pattern to spend some time really looking at it and sharing ideas with someone else. All patterns have some element of repetition, and it is interesting to hear what unit people think is the basis for the repeated element. The book identifies this as a line that travels around the edge of a regular hexagon touching it at each of its vertices.

Using the program Turtle Tracks, I set out to copy this line and reduce it to a series of commands, F-forward, and R-turn right, that could be repeated six-times. This sequence of commands turned out to be: R,F,R,R,R,F,F,F,R,R,R,F,R,R,R, where R is set to an angle of 30°. This is required to be able to rotate the starting position of the turtle, and to be in the correct starting orientation at the end of the sequence. …

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