Group Theory Applications in Traditional Indian and Islamic Geometric Designs

Yajat Agarwal

Abstract: Art and mathematics have long shared a deep relationship through the language of symmetry and pattern. This paper explores how group theory-particularly the classification of symmetry groups-provides a rigorous mathematical framework to understand, analyze, and even recreate traditional Indian mandalas and Islamic geometric designs. By mapping artistic symmetries to mathematical structures such as dihedral groups, frieze groups, and wallpaper groups, we reveal how artisans historically applied mathematical reasoning intuitively. The study connects aesthetic principles with algebraic structures, offering insights into how geometry, repetition, and abstraction reflect universal mathematical ideas embedded in visual culture.

Keywords: symmetry, group theory, geometric art, tessellation, mandala, Islamic geometry, frieze groups, wallpaper groups, dihedral symmetry, cultural mathematics, mathematical aesthetics

How to Cite?: Yajat Agarwal, "Group Theory Applications in Traditional Indian and Islamic Geometric Designs", Volume 14 Issue 10, October 2025, International Journal of Science and Research (IJSR), Pages: 1119-1120, https://www.ijsr.net/getabstract.php?paperid=SR251017172534, DOI: https://dx.doi.org/10.21275/SR251017172534