The Geometry, Algebra, and Algorithms of Paper Folding
Paper folding is far more than a craft—it is a rich mathematical discipline. Origami can trisect angles (impossible with compass and straightedge), solve cubic equations, and generate rigid deployable structures used in space engineering. Explore the Huzita-Hatori axioms, Kawasaki’s and Maekawa’s theorems, Miura-ori tessellations, and modular polyhedra—all through interactive simulations built from real mathematics.
The fundamental rules that govern what is possible with a single fold. These axioms define origami as a formal mathematical system.
Explore all 7 axioms of origami construction. Place points and lines, then watch the crease appear. Each axiom aligns geometric elements in a unique way.
The standard diagramming language of origami. See each symbol—valley fold, mountain fold, sink, turn over—animated on paper with clear explanations.
Mathematical rules that determine whether a crease pattern can fold flat. These theorems are essential for origami design and computational origami.
At any vertex, alternating angles must sum to 180°. Drag crease lines and watch the angle sums update in real-time. Green vertex = flat-foldable!
Mountain and valley folds must differ by exactly 2 at every vertex. Click creases to assign fold types and verify |M - V| = 2 interactively.
Draw mountain and valley creases on a grid. The editor validates both Maekawa’s and Kawasaki’s theorems at each vertex. Load preset bases to explore.
Origami achieves geometric feats impossible with classical tools. These demos showcase the surprising power of paper folding.
From deployable space structures to decorative tessellations, these simulations show origami in action as engineering and art.
The famous fold used for satellite solar panels. Drag the slider to fold and unfold the tessellation. Adjust grid size, zigzag angle, and 3D rotation.
Panels as stiff plates, creases as hinges. Fold waterbomb bases, bird bases, and box pleats while panels remain perfectly rigid—essential for engineering.
Repeating fold patterns that tile the plane. Explore triangle, square, hexagonal, and pinwheel twists with adjustable fold depth and dynamic lighting.
Identical folded units assembled into 3D forms. Rotate, explode, and explore Sonobe cubes, stellated octahedra, icosahedra, and more.