foldandcut

Foldandcut refers to a paper craft technique that merges folding (origami) and cutting (kirigami) to create designs. The basic method involves folding a sheet of paper along a planned sequence of creases so that a single straight cut yields when unfolded a pattern that is often a symmetrical silhouette or arrangement of shapes. The approach takes advantage of how folds map parts of the paper onto one another, turning one cut into many resulting edges.

In mathematics, fold-and-cut is associated with the fold-and-cut theorem. The theorem asserts that any finite arrangement of straight-line segments can be produced from a single straight cut after folding the paper appropriately. The result was developed in the field of computational origami during the 1990s by researchers including Erik Demaine and collaborators. The theorem highlights a concrete link between origami folding operations and geometric constructions, showing that complex planar patterns can be obtained from a simple cut through careful folding.

Practically, foldandcut is used for decorative arts, stencils, valentines, and educational demonstrations of symmetry and geometry. It serves as a teaching tool to illustrate how folding creates overlap and alignment, as well as how a single action can generate many edge connections when the design is unfolded.

Limitations include that the mathematical theorem applies to straight-line segments; curved edges or filled regions may require approximations, multiple cuts, or iterative folding. In craft contexts, designers often adapt folds and may combine folds with multiple cuts for more complex imagery. Related topics include origami, kirigami, and computational origami.