Folding

Folding refers to the act of bending or layering a material so that it takes a shape with a smaller footprint or different geometry. It can be a manual craft, a geometric operation, or a natural process.

In arts and crafts, paper folding is the practice of folding sheets to create decorative or representational forms. Origami, which originated in East Asia, focuses on precision creases and unfolding to reveal complex structures. In textiles and packaging, folding achieves creases, pleats, and compact forms.

In geometry and mathematics, folding is studied as a transformation or construction. crease patterns specify where folds occur, and various models address how a flat sheet can be folded into three-dimensional structures, including rigid origami where faces remain planar. Problems explore whether a given pattern can be folded from a single piece of material and how to realize folds with minimal soft or hard constraints.

In biology, protein folding describes how a linear chain of amino acids assumes a functional three-dimensional structure. Folding is guided by intramolecular forces and assists from chaperone proteins. Misfolding can cause loss of function or aggregation and is linked to diseases such as Alzheimer's and cystic fibrosis.

In computing, folding can refer to a fold operation in functional programming, which reduces a sequence to a single value by iteratively applying a function. The concept also appears in data compression and in the visualization of hierarchical data, where layouts fold or unfold sections to manage complexity.

Other uses include foldable structures in engineering, architecture, and space-saving design, where folding enables compact storage or dynamic form changes.