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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).
A dashed line shows a valley fold. The paper is folded in front of itself. A dashed and dotted line shows a mountain fold (there may be one or two dots per dash depending on the author). 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.
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 ...
Strip folding is a combination of paper folding and paper weaving. [30] A common example of strip folding is called the Lucky Star, also called Chinese lucky star, dream star, wishing star, or simply origami star. Another common fold is the Moravian Star which is made by strip folding in 3-dimensional design to include 16 spikes. [30]
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]
Pages in category "Paper folding" The following 37 pages are in this category, out of 37 total. This list may not reflect recent changes. * Origami; Paper craft; B.
The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin can increase its perimeter. The problem is known under several names, including the Margulis napkin problem , suggesting it is due to Grigory Margulis , and the Arnold's rouble problem referring ...
In the mathematics of paper folding, map folding and stamp folding are two problems of counting the number of ways that a piece of paper can be folded. In the stamp folding problem, the paper is a strip of stamps with creases between them, and the folds must lie on the creases. In the map folding problem, the paper is a map, divided by creases ...