A flat sheet folds step-by-step into a simple origami box, holds, then unfolds and loops.
Origami is the traditional Japanese art of paper folding, though independent paper-folding traditions also arose in China and Europe. Classical origami follows a "no cuts, no glue" rule: a single uncut square of paper is transformed into a finished form using only folds. Every fold is one of two basic types — a mountain fold (crease pointing away from you, like a peak) or a valley fold (crease pointing toward you, like a trough) — and sequences of these are recorded in standardized diagrams using dashed and dash-dot lines. Beyond crafts, the geometry of folding has become a serious branch of mathematics and engineering, studied because flat sheets can pack into small volumes and deploy into large, precise structures. This has made origami principles directly useful for real hardware, from spacecraft to medical devices.
- Traditional origami uses no cuts and no glue — only folds on a single sheet.
- Maekawa's theorem: at any flat-foldable vertex, the number of mountain and valley folds always differs by exactly two.
- A crease pattern is "flat-foldable" only if it satisfies strict mathematical rules (Maekawa's and Kawasaki's theorems).
- Engineers used origami-inspired folding to design the accordion-style deployment of the Miura-ori solar panel array flown on Japanese satellites.
- Origami folding patterns have inspired compact folding car airbags and expandable medical stents that unfold inside blood vessels.
- Common origami papers include thin "kami" (colored one side), and foil-backed paper that holds sharper creases.
- Origami's documented history traces to Japan after paper-making arrived from China around the 6th century, with ceremonial folding recorded by the 1600s.
- Modern computational origami software can algorithmically generate crease patterns for astonishingly complex, realistic figures.