Geometry and Pattern in Seljuk and Ottoman Architecture

Course data in brief

Instructor: Prof. Dr. Miroslaw Majewski

Course duration: 15 weeks, 2 hours per week + discussion time, with 2 weeks break for Christmas and New Year

Course timing: Fridays

6:00 PM GMT, UK Time,

7:00 PM Cairo Time,

8:00 PM Istanbul Time,

9:30 PM Tehran Time, …

Course starting day: 08 October, 2021

Language: English and no translation (sorry),

Level: intermediate,

Group size: 30-60 persons, please register at the IDC web site:

Essential features of the course:

• All coursework in Geometer’s Sketchpad – the essential software for teaching school geometry

• Focusing on concepts and understanding of pattern design

• Strict attendance rules

• Free of charge – there is no fee for this course

• International group

• Online delivery

What should you expect?

This course will be focusing on geometric aspects of mostly decagonal patterns from various places in the western part of the Seljuk Empire and Ottoman Empire. Numerous designs from this region will be used as an illustration of geometric concepts.

We will use the traditional gereh method that was used in the XV-XVIII centuries by architects and craftsmen from Central Asia and Iran.

For each example, we will start by finding the proportions of the template, then we will create the geometry of the pattern, and finally, we will add to it its decoration - the pattern.

No pain, no gain

The course will be demanding, and you will be expected to demonstrate your progress in the form of finished designs. You will have to submit them always before the next class.

Feel free to ask questions and discuss with us anything related to this course. There are no silly questions. Each question may lead to an exciting discussion and forming valuable knowledge.

Important – if you miss two classes, you will be removed from the course.

Geometry goes first

The focus of this course will be on the geometry of patterns - not on particular designs. Understanding and creating geometry for a pattern or group of patterns will always be the two main tasks. Patterns will be treated as a decoration for geometry.

Geometer’s Sketchpad

In each class of the course, Geometer’s Sketchpad (GSP) will be essential for all our works. It is much easier to learn geometry and pattern design with a geometry program and then do your art using traditional tools. For this reason, this course can be in particular useful for mathematics teachers.

You can download GSP from

The license for it, you will get during the first class. Before starting the course, you have to figure out how you can handle on your computer screen two tasks at the same time – listening and watching the course and at the same time drawing on your screen. This will be the tricky part. Of course, you can forget about Sketchpad and draw by hand on paper. But this is the only course where you can learn how to use Sketchpad to draw patterns.

If you know GeoGebra and you want to stick to it. This is OK. But you are on your own. I will not be able to help you with using GG.

After geometry comes art

We will discuss forms of artistic interpretations of patterns. Thus we will talk about patterns made of ceramic tiles, carving patterns in wood and stone, Ottoman kundekari designs, developing structures, etc.

If time permits, we may have short virtual excursions to some places in Turkey.

Possible topics

1. Learning how to use Geometer’s Sketchpad

2. Basic geometric constructions (of course with Sketchpad) esp. constructions related to decagonal geometry

3. Specific features of Seljuk decagonal designs

4. Specific features of Ottoman decagonal designs

5. Exploring structures in Ottoman decagonal designs

6. Introduction to some unusual Ottoman designs

Teacher and students

Miroslaw Majewski (Prof. Dr) is a former Professor of the New York Institute of Technology. Currently, Professor Emeritus of NYIT. Many years of research in the geometry of art and technology for mathematics. Author of numerous books and publications (many of them related to the geometry of patterns). Designer of many geometric patterns – some are reconstructions of well-known patterns, and some of them are entirely new.

Students: This is an academic level course, and it fits nicely into some university programs – graphics design, architecture, mathematics education. Thus mathematics teachers and professional artists, and architects are particularly welcomed. Anybody ready to work hard and learn the theory of pattern design will find in this course some useful knowledge.

If you are interested only in drawing a few simple patterns (just to impress your friends), then find yourself another course. There are a few of them around.

Before starting the course

You may consider looking at some books. You will find there some important fundamentals useful for this course. In the first book, foundations of geometric pattern design are covered. The second book covers material from the fall 2020 course on Persian decagonal artworks.

You may consider looking at the book

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