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The Huzita–Justin axioms or Huzita–Hatori axioms are a set of rules related to the mathematical principles of origami, describing the operations that can be made when folding a piece of paper. The axioms assume that the operations are completed on a plane (i.e. a perfect piece of paper), and that all folds are linear.
Modular origami or unit origami is a multi-stage paper folding technique in which several, or sometimes many, sheets of paper are first folded into individual modules or units and then assembled into an integrated flat shape or three-dimensional structure, usually by inserting flaps into pockets created by the folding process. [3]
A Kunai normally had a leaf-shaped wrought blade in lengths ranging from 20 and 30 cm (7.9 and 11.8 in) and a handle with a ring on the pommel for attaching a rope. The attached rope allowed the kunai's handle to be wrapped to function as a grip, or to be strapped to a stick as a makeshift spear; to be tied to the body for concealment; to be used as an anchor or piton, and sometimes to be used ...
The paper is folded behind itself, this is normally done by turning the paper over, folding a valley fold and then turning the paper back over again. A thin line shows where a previous fold has creased the paper. A dotted line shows a previous fold that's hidden behind other paper, or sometimes shows a fold that's not yet made.
The fold-and-cut theorem states that any shape with straight sides can be cut from a single (idealized) sheet of paper by folding it flat and making a single straight complete cut. [1] Such shapes include polygons, which may be concave, shapes with holes, and collections of such shapes (i.e. the regions need not be connected ).
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For rigid origami (a type of folding that keeps the surface flat except at its folds, suitable for hinged panels of rigid material rather than flexible paper), the condition of Kawasaki's theorem turns out to be sufficient for a single-vertex crease pattern to move from an unfolded state to a flat-folded state.
The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability (whether the model can be flattened without damaging it), and the use of paper folds to solve mathematical equations up to the third order. [1]