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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 ).
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 ...
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 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.
En papillote (French pronunciation: [ɑ̃ papijɔt]; French for "enveloped in paper" [1]), or al cartoccio in Italian, is a method of cooking in which the food is put into a folded pouch or parcel and then baked. This method is most often used to cook fish or vegetables, but lamb and poultry can also be cooked en papillote.
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In the mathematics of paper folding, the big-little-big lemma is a necessary condition for a crease pattern with specified mountain folds and valley folds to be able to be folded flat. [1] It differs from Kawasaki's theorem , which characterizes the flat-foldable crease patterns in which a mountain-valley assignment has not yet been made.
1. Lay the towel vertically on a flat surface, tag side up. 2. Make a small fold from the bottom (the side nearest you), turning under a section of towel about the width of your palm.