Geometric Patterns for Absolute Beginners


A five days course on geometry and pattern design offered by the Istanbul Design Center, School of Geometric Patterns in Islamic Arts

Instructor: Prof. Dr Miroslaw Majewski

Course Data in Brief

• Location: İstanbul Desing Center

• Course duration: 5 days, 4-5 hours per day, plus excursions through mosques in Istanbul

• Dates: 20 – 24 June 2022

• Course Hours: 10.00 am – 04.00 pm (Course hours include sightseeing walks as well. The mosques in Istanbul's Fatih district will be visited on foot, for about 3 or 4 hours a day.)

• Language: English with translation into Turkish

• Level: basic

• The form: a face-to-face in the classroom

• Media: a free version of computer software Geometer’s Sketchpad (bring your laptop)

• Group size: 25 participants.

A laptop is needed with Geometer's Sketchpad software installed.

What Should You Expect?

This will be a technology-based course. All works will be done with computer software – Geometer’s Sketchpad (GSP). Therefore, you will need to bring your laptop, with Windows or Mac operating system. Before starting the course, we will check the GSP installation on your laptops. Then each project will be done using this software.

Geometer’s Sketchpad is a very popular and simple tool for teaching primary and secondary school geometry. It imitates how we make constructions using pencils, rulers, and compasses. Thus we draw lines, circles, and polygons. We make geometric operations exactly the same way as we did it in the school. Then we paint our objects the same way as kids paint their pictures. There are two major advantages of using GSP: (1) multiple pages in one file will allow you to go back to any of the previous stages of your construction and develop it differently; (2) custom tools will save your time by allowing you to copy fragments of older constructions into your current work.

However, if you still prefer to do your drawings by hand, you are welcome. But, drawing patterns with GSP is much faster, and you may find yourself quite behind your classmates.

Geometer’s Sketchpad Versions

At the very moment (20/04/2022), there are three versions of Geometer’s Sketchpad.

MAC : Mac version can be downloaded and installed from the website

This is complete software—no need for a license number.

Windows : There are two Windows versions. For this course we will use the one with the proper installation procedure and proper help system. This one can be downloaded from the

Here is the license key for it: The license key will be shared with the participants before the course.

Geometry in Pattern Design

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. We will follow the steps of pattern design that are documented in scrolls of medieval pattern designers and architects.

After Geometry Comes Art

We will discuss forms of artistic interpretations of patterns. Thus we will talk about patterns made in ceramic tiles, carving patterns in wood and stone, Ottoman kundekari designs, developing structures, etc. We will learn how one can draw designs reflecting patterns from mosques, tombs, and madrasahs. As a source of inspiration, we will use real objects. Thus we will often go to visit some mosques in Istanbul.

Possible Topics

1. Learning how to use Geometer’s Sketchpad

2. Basic geometric constructions with Sketchpad

3. Using color and textures

4. Developing patterns on triangular and square grids

5. Patterns with 6, 9, and 12 fold symmetries

6. Patterns with stars and rosettes

7. Octagonal patterns from East Asia and Iran

8. Octagonal patterns from Maghreb

9. Decagonal Persian and Ottoman origin

Teacher and Students

Miroslaw Majewski (Prof. Dr) is a former Professor at 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 introductory course and anybody interested in drawing geometric patterns can enter it and learn a lot. This course can be very useful for high school and university students as well as mathematics teachers.


Here are some patterns made by students from previous courses.