In the footsteps of Seljuk geometry: Mathematical symmetry analysis and digital reconstruction of geometric patterns in mosques of Kastamonu

The objective of this thesis is twofold: Firstly, to analyse the mathematical symmetry properties of geometric patterns found in the mosques of Kastamonu from the Seljuk and Beylik periods; secondly, to digitally reconstruct them using GeoGebra software. In addition, the philosophical background of geometric pattern choices will be revealed, thereby uncovering the architectural aesthetics and mathematical structure of these historical buildings from an interdisciplinary perspective. Three mosques that have preserved their originality (Atabeygazi Mosque, Yılanlı Mosque, and Mahmutbey (Kasaba) Mosque) were examined on-site, their patterns photographed and analysed within the framework of the 17 plane symmetry groups standardized by the International Union of Crystallography. During the analysis, fundamental types of symmetry such as translation, rotation, reflection, and glide reflection were taken into account, and a method was developed based on the flowchart proposed by Horne. The symmetry codes of the patterns were identified through this method. Furthermore, the patterns examined in this study were compared with those in Ekizler's work, and it was determined that they show a high degree of similarity. However, it was also identified that certain patterns, namely Mihrap-1 (p4mm) in Atabeygazi Mosque, and Kasaba-4 (p4mm), Kasaba-5 (p4mm), Kasaba-6 (p31m), and Kasaba-7 (p6mm) in Kasaba Mosque, present new compositional arrangements that are not included in Ekizler's study. Based on these findings, it is evident that the understanding of geometric ornamentation characteristic of the Seljuk and Beylik periods continued in the mosques of Kastamonu and that these structures reflect the artistic perspective of the Seljuk tradition. The results of the study demonstrate that geometric patterns are not merely aesthetic elements, but that they also function as an arrangement imbued with mystical, philosophical and symbolic meanings within Islamic thought. In this respect, the present study makes a significant contribution to the existing body of literature by offering new insights and perspectives on the subject