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The construction of origami models is sometimes shown as crease patterns. The major question about such crease patterns is whether a given crease pattern can be folded to a flat model, and if so, how to fold them; this is an NP-complete problem. [32] Related problems when the creases are orthogonal are called map folding problems.
The Miura fold (ミウラ折り, Miura-ori) is a method of folding a flat surface such as a sheet of paper into a smaller area. The fold is named for its inventor, Japanese astrophysicist Kōryō Miura. [1] The crease patterns of the Miura fold form a tessellation of the surface by parallelograms.
Crease pattern for a Miura fold. The parallelograms of this example have 84° and 96° angles. The Miura fold is a rigid fold that has been used to pack large solar panel arrays for space satellites, which have to be folded before deployment. Robert J. Lang has applied rigid origami to the problem of folding a space telescope. [7]
A quilled basket of flowers. Paper craft is a collection of crafts using paper or card as the primary artistic medium for the creation of two or three-dimensional objects. . Paper and card stock lend themselves to a wide range of techniques and can be folded, curved, bent, cut, glued, molded, stitched, or layere
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 ).
The pattern figure can be drawn by pen and compass, by creating seven interlinking circles of the same diameter touching the previous circle's center. The second circle is centered at any point on the first circle. All following circles are centered on the intersection of two other circles.
The map folding and stamp folding problems are related to a problem in the mathematics of origami of whether a square with a crease pattern can be folded to a flat figure. If a folding direction (either a mountain fold or a valley fold ) is assigned to each crease of a strip of stamps, it is possible to test whether the result can be folded ...
The pattern can be extended outward in concentric hexagonal rings of circles, as shown. The first row shows rings of circles. The second row shows a three-dimensional interpretation of a set of n×n×n cube of spheres viewed from a diagonal axis. The third row shows the pattern completed with partial circle arcs within a set of completed circles.
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