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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).
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.
Maekawa's theorem is a theorem in the mathematics of paper folding named after Jun Maekawa. It relates to flat-foldable origami crease patterns and states that at every vertex, the numbers of valley and mountain folds always differ by two in either direction. [1] The same result was also discovered by Jacques Justin [2] and, even earlier, by S ...
Geometric Origami is a book on the mathematics of paper folding, focusing on the ability to simulate and extend classical straightedge and compass constructions using origami. It was written by Austrian mathematician Robert Geretschläger [ de ] and published by Arbelos Publishing (Shipley, UK) in 2008.
Download as PDF; Printable version; ... This category is for origami, the Japanese art of paper folding. ... Chinese paper folding; Crease pattern; D.
The placement of a point on a curved fold in the pattern may require the solution of elliptic integrals. Curved origami allows the paper to form developable surfaces that are not flat. [41] Wet-folding origami is a technique evolved by Yoshizawa that allows curved folds to create an even greater range of shapes of higher order complexity.
Printable sheet to make a metro train of the Valencia Metro (Venezuela). This may be considered a broad category that contains origami and card modeling. Origami is the process of making a paper model by folding a single piece of paper without using glue or cutting while the variation kirigami does.
Origami paper and a traditional origami crane. Origami paper is the paper used for origami, the art of Japanese paper folding.The only real requirement of the folding medium is that it must be able to hold a crease, but should ideally also be thinner than regular paper for convenience when multiple folds over the same small paper area are required (e.g. such as would be the case if creating an ...