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Folding endurance is especially applicable for papers used for maps, bank notes, archival documents, etc. The direction of the grain in relation to the folding line, the type of fibres used, the fibre contents, the calliper of the test piece, etc., as well as which type of folding tester that is used affect how many double folds a test piece ...
With each fold a certain amount of paper is lost to potential folding. The loss function for folding paper in half in a single direction was given to be L = π t 6 ( 2 n + 4 ) ( 2 n − 1 ) {\displaystyle L={\tfrac {\pi t}{6}}(2^{n}+4)(2^{n}-1)} , where L is the minimum length of the paper (or other material), t is the material's thickness, and ...
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 ).
Origamics: Mathematical Explorations Through Paper Folding is a book on the mathematics of paper folding by Kazuo Haga [], a Japanese retired biology professor.It was edited and translated into English by Josefina C. Fonacier and Masami Isoda, based on material published in several Japanese-language books by Haga, and published in 2008 by World Scientific. [1]
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 ...
Heighway dragon curve. A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.The dragon curve is probably most commonly thought of as the shape that is generated from repeatedly folding a strip of paper in half, although there are other curves that are called dragon curves that are generated differently.
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 regular paperfolding sequence corresponds to folding a strip of paper consistently in the same direction. If we allow the direction of the fold to vary at each step we obtain a more general class of sequences. Given a binary sequence (f i), we can define a general paperfolding sequence with folding instructions (f i).