TAGRA 2025

When we look at traditional arts, we see that throughout history, they have been shaped not only by aesthetic concerns but also by specific mathematical principles and ratio systems, creating a unique field of expression where science and art intertwine. The concepts of rhythm, repetition, symmetry, proportion, and order seen in Turkish-Islamic arts such as calligraphy, illumination, miniature, tile-making, marbling, and geometric ornamentation are concrete examples of the invisible yet decisive influence of mathematics on the visual field. The purpose of this paper is to uncover the mathematical structure underlying traditional arts and to evaluate the aesthetic and technical functions of these structures in artistic production. In calligraphy, the measurements, angles, and line arrangement of letters are based on strict rules. The proportions between letter lengths, particularly in Thuluth and Naskh script, are created according to a specific geometric system. In illumination art, the construction of hatai, rumi, penç, and geometric interlaced motifs is shaped by the Golden Ratio, axes of symmetry, and polygonal-based divisions. Circle, star, and polygonal arrangements are transformed into repetitive surfaces that evoke a sense of infinity through digital multiplication methods. The concept of multiple perspective used in miniature art is created by placing figures and spatial distributions within a mathematical order. In tile art, octagonal, decagonal, and hexagonal interlaces create geometric systems that provide surface continuity through a fractal-like growth logic. The techniques of division, folding, symmetry transformations, and proportioning used in the creation of traditional patterns parallel contemporary design mathematics. Consequently, mathematics in our traditional arts is not only a creator of order but also an aesthetic and visual language. This study aims to reveal the scientific structure behind artistic production by evaluating the fundamental formations of traditional arts and mathematics from an interdisciplinary perspective.