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Geometric Patterns: The Visual Testament of Islamic Civilizations

This 25-week-long intermediate-level course will allow students to gain a perspective in analyzing geometrical patterns, a historical awareness of Islamic civilizations, and foundational knowledge of science and art history.

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Geometric Patterns: The Visual Testament of Islamic Civilizations
Geometric Patterns: The Visual Testament of Islamic Civilizations

Time & Location

Sep 10, 2022, 5:00 PM UTC


Course Details


Date Range: September 10, 2022 - March 18, 2023

Time: 5 PM UTC 

Course Format: Online (Zoom) Recordings will only be available for those with excused absences.

Duration of a lesson:1.5 hours, weekly (occasionally the class may go over time)

Course finances:  Installment plans available [click to request] 

Skill Level: Intermediate

Age Range: 18+

Course Instructor: Dr. Serap Ekizler Sönmez (Geometer/Artist/ Historian of Islamic Architecture)


The examples of geometric ornamentations found mainly in architecture, almost everywhere in the Muslim world, are testaments to great Islamic civilizations of the past. Learning from these and specifically looking at the middle ages, we can understand the civilizations and their span. Although there are studies on this topic, they fall short in evaluating the subject in the context of the history of Islamic civilizations, analyzing the richness of the compositions mathematically, and keeping the geographical conditions in mind. It is also not sufficient to point out the physical existence of the geometrical patterns within the Islamic sciences, geometry, algebra, architecture, art history, history of science, philosophy, and even physical sciences such as physics, chemistry, and biology. Instead, they should be explored holistically within the given multidisciplinary frame. Only then, questions such as the nature of the triangular relationship of the artisan-scientist-craftsman, the way patterns are produced, and the methods used by the craftsman when employing a given pattern can come to light. Otherwise, something will always be missing. The extent to which patronage is essential in producing works of art is another question that needs to be addressed. The fact that science and art flourish when supported is known to everybody.

With all this in mind, this class will provide a framework to understand the dynamics of Islamic civilizations. As we study this field, an artistic manifestation of science, students will gain foundational knowledge of the history of science and art, a perspective in analyzing geometrical patterns, and understanding the history of the Islamic civilizations.


1- Introduction to geometrical patterns

2- Six-fold (hexagonal) geometrical patterns

2.1. Constructing a triangle and a hexagon.

2.2. The geometry of a hexagon and symmetry

2.3. Construction with a ruler and a compass and pattern analysis through an isometric grid system

2.4. Triangular grid patterns employed in pre-Islamic societies.

2.5. The perception of hexagonal stars across different religions.

2.6. The transmission of hexagonal patterns in early Islamic art to Anatolia and their reflections in the classical Ottoman era.

2.7. Examples of six and twelve pointed stars in a hexagon unit cell and a root-3 rectangle cell.

2.8. Six-pointed star patterns with different corner angles, their relation to each other, and new designs.

2.9. Relationships between six-fold symmetrical designs.

2.10. A famous example of grid pattern from the works of Sinan and its construction. Learning the systems behind this pattern and gaining skills to derive unique patterns by comparing these patterns.

3. Four-fold (Square form) Geometric Patterns

3.1. Constructing a square

3.2. Description of a four-fold pattern and symmetry.

3.3. Construction with a ruler, compass, and pattern analysis through an isometric grid system.

3.4. Identifying a square unit cell.

3.5. Patterns that emerge from a square and relationships between these patterns.

3.6.Four-fold forms with different points of origin.

3.7. Four-fold patterns used in pre-Islamic societies

3.8. Examine the differences between the fourfold patterns in Spain and Maghribi Anatolia and their modular systems.

3.9. The square unit cell of the Anatolian Seljuk patterns and differences in application.

3.10. Central Asian modular systems.

3.11. Six-fold pattern designs with square unit cells.

4. Five-fold Geometric Patterns

4.1. From the golden triangle to the golden ratio

4.2. Penrose tiles

4.3. The properties of a pentagon

4.4. The difference between five-fold systems from others, the notion of modular form, and the designs that make up the basis of the pentagonal structure systems.

5. Primary Islamic sources on Geometric patterns

6. Evaluating the historical and regional changes of the geometric patterns and the differences in the methods of their use from an aesthetic point of view

7. Contemporary studies, scholars, publishings [in the field], and the role of the Islamic world

8. The possibility of building a common civilization from geometric designs?


At the end of this workshop, students will learn basic geometric structures of geometrical patterns. They will be able to analyze, at a basic level, a geometric pattern they may encounter. Additionally, they will have an understanding of the history of Islamic architecture. They will realize the developments and the changes in the materials and the conception of the designs across different regions. With the knowledge of the history of science, students will gain awareness of a civilization that has produced an advanced level of science. In addition, they will recover their confidence in their Islamic heritage. Finally, with the knowledge of the history of art and architecture and the study of specific works, the students will dig the notion of tawhid (oneness) in Islamic aesthetics and understanding of Islamic arts.

*Benefiting from multiple disciplines, this unique academic and systematic program is designed especially for DeenArts Foundation.

*Participants will receive a certificate at the end of the program.

Materials List:

Due to limited seating, we request you cancel by August 1,  2022, to receive a full refund.

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