Islamic Geometric Ornaments in Istanbul

Setting the goal – Islamic ornaments are one of the greatest achievements of ancient geometers, artisans and craftsmen in the Middle East, Turkey, India, Spain, and North Africa.  These ornaments are frequently used to decorate sacred, secular and private buildings, books, and furniture. Istanbul, in particular, is a place where such ornaments were, and still are, frequently used.

In this book we will explore selected geometric ornaments from Istanbul. Many of these ornaments can be created by using very precise geometric constructions. We will analyze the structure of these ornaments and show how grids used to draw these ornaments, were constructed. A computer program, The Geometer’s Sketchpad, will be used to construct these grids as well as complete ornaments. In a few examples a computer graphics program will be used to add some finishing touches to our work. Many of the examples presented in this book have a significant cognitive value. While creating them we can learn a number of important topics in geometry, e.g., constructions of regular polygons, constructions of figures circumscribed or inscribed in a circle, division of angles and segments into a given number of parts, transformations of figures, a touch of symmetry groups,  and a number of other topics.

Organization – There are four major parts in this book. In the first part we will refresh some important facts of the history of Islam and Islamic art. In the second part we will revise our knowledge of geometric constructions. The third part of this book can be considered as a mathematical tour through some places in Istanbul. I will be your guide and we will walk together through some of my favorite places in this ancient city. We will walk through the famous Blue Mosque, Hagia Sophia, Şehzade Mosque, and a few other places. Finally, in the appendix of this book I will show how a computer program for geometry can be used to construct Islamic geometric ornaments. However, I will concentrate on one computer program only – The Geometer’s Sketchpad.

In literature there is quite a lot of talk about cosmological aspects of Islamic geometric ornaments. In this book we will not explore this area. We will concentrate mostly on the geometry of Islamic geometric ornaments, explore ways how they can be constructed, and we will confine ourselves to Istanbul.

Thank you – I would like to express my gratitude to the many people who have helped me to write this book, encouraged my efforts, and sometimes even tested some of my constructions. Among those that must be especially mentioned are my friends Linda Graham, Bogumiła Klemp-Dyczek,
Kamal Al-Achrafi, Andrzej Nowicki Steven Rasmussen, Scott Steketee, Erol Karakirk, Sammein Gündüz, and many others.

For whom is this book? You probably wonder if this really is a book for you. Well, I didn’t have any particular audience in my mind when I started this project. My intention was to show how the two eternal beauties, mathematics and art, can interact and give us something that is admired by millions of people in our world. This is a book on mathematics and art. Therefore if you are not a mathematician, or your mathematical skills are not first rate – you do not need to worry, there is no heavy mathematics in this book; if you are an artist then certainly you can use this book as a source of inspiration for your works; if you are a teacher of mathematics this book will give you some ideas for your classroom; if you are a student you can learn that mathematics can be found around you even in the most unexpected places; finally if you do not belong to any of these groups just have a little pleasure seeing something that many people love so much.

I invite you to join me on this mathematical tour through Istanbul.

Mirek Majewski, Abu Dhabi – Istanbul – Toruń, Spring – Summer, 2011.