Prayer Maths Author(s): Taheer Kasmani Source: Mathematics

Prayer Maths

Author(s): Taheer Kasmani

Source: Mathematics in School , Jan., 2007, Vol. 36, No. 1 (Jan., 2007), pp. 16-18

Published by: The Mathematical Association

Stable URL: https://www.jstor.org/stable/30215981

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https://www.jstor.org/stable/30215981

Pra maths by Taheer Kasmani

Introduction

Mathematics in my mind is the language of the world. Euclid was Greek, fractions originated in Egypt and an Englishman solved a Frenchman's Last Theorem. Mathematics is the

heart of the world. The world is governed by nature, which is ruled by laws that are formulated by physics, which only exists because of mathematics. So why are there pictures of carpets and architecture? Why not a huge figure of pi?

Well, believe it or not, these pictures are related by two factors. The first is easy to recognize if you are Muslim, have been to a Middle Eastern Country, visited a Mosque or have Muslim friends. They are all prevalent in the Muslim World.

The second connection is mathematics (after all this is a mathematics journal!). Look again at the carpet but this time concentrate on the border. Look at the star, can you see that it is repeating itself. What you are looking at is called a frieze pattern.

Frieze Pattern

A frieze is a pattern obtained by repeating some basic unit over and over again in one direction (Stewart, 1998, p.122). Mathematical analysis has revealed that there are only seven frieze patterns which are created by different combinations of symmetries on the basic unit. These can be seen below. Frieze patterns decorate the world around us and can be found in architecture and furniture. They are also prevalent in the Muslim World but in what way do these frieze patterns and the art of Islam differ to some of the world's cultures? Well, the root of Islamic Art lies in mathematics and geometry. As El-Said and Parman point out (1976, p.3) "In the construction of Islamic crafts ... the compass and the ruler are the only major instruments used."

Mathematics in the Prayer Mat

The border patterns found in a lot of prayer mats are constrained to the seven frieze groups. The frieze pattern that appears below is a copy of the border of the prayer mat seen on the front cover. Can you guess which group it

F, Group: Translational symmetry F2 Group: Translational and glide symmetries

F3 Group: Translational and vertical symmetries

F, Group: Translational and rotation symmetries

F, Group: Translational, glide reflection and rotation symmetries

F6 Group: Translational and horizontal symmetries

F, Group: Contains all four symmetries

16 Mathematics in School, January 2007 The MA web site www.m-a.org.uk



belongs to? Regular stars, as seen in the border, are commonly used as decoration throughout the Muslim World.

As well as frieze patterns, prayer mats also contain tessellations and wallpaper patterns. Tessellations are also prevalent in carpets, courtyards and buildings such as mosques.

Mathematics in the Mosque

The frieze pattern that appears below can be found in the Ilyas Bey Mosque in Balat in Turkey. The pattern is copied from an illustration by Field (2004, p.15). Field's book is absolutely delightful! I recommend it for anyone who wishes to learn more about the geometric patterns found in Islamic Art and Architecture. Each page is filled with

photographs, alongside which Field has recreated the geometrical designs. All can be drawn with squared or isometric paper making the impossible easy to follow.

Also copied from Field (2004, p.55) is the frieze below. The frieze pattern is from Konya in Turkey. Can you determine which frieze groups these two patterns belong to?

The frieze at the top of the next column details one of the brick patterns found in the Chihil Dukhteran Mausoleum in Iran (Albarn et al., 1974, p.41). Once again do you have any idea which frieze group this pattern belongs to?

Mathematics in the Quran

By the title I do not mean that there is mathematics in the Quran, although one cannot be sure. What I am actually referring to is the mathematics found in the borders and the actual Quran script also known as Arabic calligraphy.

The frieze pattern below is a modification of a design that is taken from the ribbon interlace of a Quran produced in Cairo in 1304 (Wilson, 1997, design 52).

The frieze pattern on the following page is a calligraphy frieze. According to Khatibi and Sijelmassi (1994) the art of calligraphy is also founded by a code of geometric and decorative rules. The pattern is in the form of the Arabic Kufic Script. The transliteration of the first three letters from right to left at the top right-hand corner is t, h and r. Yes, this frieze is a pattern decorating my name in Arabic.

Conclusion

At this point you will realize that you are reading the last section of this article and you are probably asking yourself two questions:

Mathematics in School, January 2007 The MA web site www.m-a.org.uk 17



"Did I guess the frieze groups of the six patterns correctly?" and "Where is the drawing of the seventh frieze pattern?"

The frieze groups of the six patterns are; Pattern 1 - F7 Group, Pattern 2 - F, Group, Pattern 3 - F, Group, Pattern 4 - F4 Group, Pattern 5 - F6 Group and Pattern 7 - F, Group. Did you get all six right?

Therefore, the frieze pattern that is missing belongs to the F2 Group. So why is it not included in the article? Well, as you are reading this journal you must have some interest in mathematics and you should know that mathematical

knowledge does not increase through osmosis. Let me rephrase that; to learn mathematics you have to do mathematics and to fully understand frieze patterns you have to get your pencil (or mouse) and draw one for yourself! Only then will you appreciate the wonders of frieze.

Overall I hope you have enjoyed this article. The purpose of it was to open your world, as well as mine, to the wonders of Islamic Geometry. I also hope that, from reading this, the next time you walk past a frieze pattern you stop, turn around and admire its mathematical beauty. For as Al-Hashimi (2003, p.55) relates, the beloved Prophet of Islam (PBUH) said:

...Allah is beautiful and loves Beauty!

References

Albarn et al. 1974 The Language of Pattern, Thames and Hudson, London. Al-Hashimi, M.A. 2003 The Ideal Muslim, 2nd edn, International Islamic

Publishing House, Riyadh. El-Said, I. and Parman, A. 1976 Geometric Concepts in Islamic Art, Scorpion

Publishing, Guildhall. Field, R. 2004 Geometric Patterns from Islamic Art and Architecture, Tarquin

Publications, Norfolk. Khatibi, A. and Sijelmassi, M. 1994 The Splendour of Islamic Calligraphy,

Thames and Hudson, Italy. Stewart, I. 1998 The Magical Maze, 2nd edn, Phoenix, UK. Wilson, E. 1997 Islamic Designs, British Museum Press, UK.

Keywords: Frieze patterns; Islamic geometry.

Author

Taheer Kasmani, St Martin's College, Bowerham Road, Lancaster LAl 3JD. e-mail: [email protected]

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Prayer Maths Author(s): Taheer Kasmani Source: Mathematics