What mathematical principles guide the folding of fabric into abstract shapes?

The art of folding fabric into abstract shapes is deeply rooted in mathematical principles, particularly those derived from origami geometry and textile design. At its core, this process relies on concepts like symmetry, tessellation, and topological transformations. Geometric algorithms guide how folds intersect and create complex patterns, while material properties such as elasticity and thickness influence the final form. Techniques like pleating, crumpling, and modular folding often employ mathematical models to achieve precision and aesthetic appeal. From fashion design to architectural installations, understanding these principles allows artists and engineers to push the boundaries of creativity with fabric. Key frameworks include the Miura-ori fold for efficient packing and hyperbolic paraboloids for dynamic sculptural effects. By merging math and art, fabric folding becomes a fascinating intersection of logic and expression.