Reconstruction of Five-Fold Patterns with the Concept of Key Length

Abstract

Art, architecture, music and literature, which are thought to be far from mathematics, contain complex mathematics. The fact that Anatolian lands hosted many civilizations throughout history provided cultural richness including the relationship between mathematics and art and created Anatolian culture. Geometric patterns are frequently encountered in artistic and architectural works in Anatolian culture. Geometric patterns existing in Anatolian culture vary according to their fold. In this research, five-fold patterns have been explained mathematically by introducing the ‘Key Length’ concept. We developed a system that reconstructs an existing Islamic Geometric Pattern in the context of the girih mode that we presented verbally and visually in eleven steps. In addition, we introduced to the literature the concept of ‘Key Length’ which is used in the drawing process.