Islamic Geometric Patterns: A Fresh Perspective

In this course, we explore the geometric foundations and methods for constructing Islamic geometric patterns. The first chapter covers the basics of geometry; the second and third chapters focus on designs with 4‑fold and 8‑fold symmetry; the fourth chapter discusses patterns with 6‑fold and 12‑fold symmetry; and the fifth chapter is dedicated to designs with 5‑fold and 10‑fold symmetry.
Chapter six is devoted to curvilinear designs, and in chapter seven we explore mixed patterns and uncommon symmetries (such as 9‑fold, 11‑fold, and 14‑fold symmetry).
In all chapters, numerous exercises are provided. Most of the examples are drawn from the style of the eastern Islamic regions (Iran and its neighboring countries).
Three main methods are used for constructing patterns: directly drawing the repeating unit with ruler and compass, using a sub‑pattern, and arranging the primary motifs. In each case, the method chosen is the one most likely to resemble the techniques originally used by the architects who first developed these designs.
Some of the methods are taken from historical texts and from the works of contemporary traditional masters in Iran, while the remaining methods are based on my own research.
All of the patterns have been drawn using GeoGebra, and the necessary tools from this software are reviewed in Chapter One. However, you can construct the patterns with a ruler and compass or with any other suitable software.