paperfolding

Paperfolding is the practice of forming three-dimensional shapes from a single sheet of paper by folding, without cutting or gluing. As an art, it is known as origami, from Japanese meaning “folding paper.” Basic folds include valley folds (creating a recessed crease) and mountain folds (creasing that rises). Complex models are made by sequences of simple folds and crease patterns.

Origins lie in East Asia, with paper arriving in China around the 2nd century CE and spreading to Japan, where folding developed into ceremonial and decorative forms. In Europe, interest grew during the 16th to 18th centuries. The modern era owes much to Akira Yoshizawa (1903–2005), who popularized diagrams with standardized symbols and advanced wet-folding to produce more lifelike shapes.

In addition to traditional designs, origami includes modular origami (assembling multiple sheets into a single model), tessellations (repeating crease patterns), and wet-folding (moistening the paper to enable curved surfaces). Kirigami introduces cuts to create openings and different geometries.

Origami intersects mathematics and engineering. The study of crease patterns and flat-foldability has yielded theorems such as Kawasaki’s, which relates to angle relationships around a vertex, and Haga’s theorems on folding squares. Modern patterns like the Miura-ori enable compact, rigid-folding panels used in space structures and deployable architectures.

Beyond art, paperfolding serves as an educational tool for geometry and spatial reasoning, and persists in cultural practices such as senbazuru, the tradition of assembling a thousand paper cranes for good fortune. Contemporary practitioners continue to develop new folds, computational methods, and applications.