Kirigami is a Japanese term for paper cutting. Cutting was often used in traditional Japanese origami, but modern innovations in technique have made the use of cuts unnecessary. Most origami designers no longer consider models with cuts to be origami, instead using the term Kirigami to describe them. This change in attitude occurred during the s and 70s, so early origami books often use cuts, but for the most part they have disappeared from the modern origami repertoire; most modern books don't even mention cutting.
Strip folding is a combination of paper folding and paper weaving. Another common fold is the Moravian Star which is made by strip folding in 3-dimensional design to include 16 spikes.
The practice and study of origami encapsulates several subjects of mathematical interest. For instance, the problem of flat-foldability whether a crease pattern can be folded into a 2-dimensional model has been a topic of considerable mathematical study.
A number of technological advances have come from insights obtained through paper folding. For example, techniques have been developed for the deployment of car airbags and stent implants from a folded position. The problem of rigid origami "if we replaced the paper with sheet metal and had hinges in place of the crease lines, could we still fold the model?
For example, the Miura map fold is a rigid fold that has been used to deploy large solar panel arrays for space satellites. Origami can be used to construct various geometrical designs not possible with compass and straightedge constructions.
For instance paper folding may be used for angle trisection and doubling the cube. With advances in origami mathematics, the basic structure of a new origami model can be theoretically plotted out on paper before any actual folding even occurs. This method of origami design was developed by Robert Lang , Meguro Toshiyuki and others, and allows for the creation of extremely complex multi-limbed models such as many-legged centipedes, human figures with a full complement of fingers and toes, and the like.
The crease pattern is a layout of the creases required to form the structure of the model.
Paradoxically enough, when origami designers come up with a crease pattern for a new design, the majority of the smaller creases are relatively unimportant and added only towards the completion of the model.
What is more important is the allocation of regions of the paper and how these are mapped to the structure of the object being designed. By opening up a folded model, you can observe the structures that comprise it; the study of these structures led to a number of crease-pattern-oriented design approaches.
The pattern of allocations is referred to as the 'circle-packing' or 'polygon-packing'. Using optimization algorithms, a circle-packing figure can be computed for any uniaxial base of arbitrary complexity. This is not a unique mathematical process, hence it is possible for two designs to have the same circle-packing, and yet different crease pattern structures.
As a circle encloses the maximum amount of area for a given perimeter, circle packing allows for maximum efficiency in terms of paper usage. However, other polygonal shapes can be used to solve the packing problem as well. The use of polygonal shapes other than circles is often motivated by the desire to find easily locatable creases such as multiples of One popular offshoot of the circle packing method is box-pleating, where squares are used instead of circles.
As a result, the crease pattern that arises from this method contains only 45 and 90 degree angles, which often makes for a more direct folding sequence. A number of computer aids to origami such as TreeMaker and Oripa, have been devised. Copyright in origami designs and the use of models has become an increasingly important issue in the origami community, as the internet has made the sale and distribution of pirated designs very easy.
It has been claimed that all commercial rights to designs and models are typically reserved by origami artists; however, the degree to which this can be enforced has been disputed.
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Under such a view, a person who folds a model using a legally obtained design could publicly display the model unless such rights were specifically reserved, whereas folding a design for money or commercial use of a photo for instance would require consent.
However, a court in Japan has asserted that the folding method of an origami model "comprises an idea and not a creative expression, and thus is not protected under the copyright law". Therefore, it is legal to redraw the folding instructions of a model of another author even if the redrawn instructions share similarities to the original ones, as long as those similarities are "functional in nature".
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The redrawn instructions may be published and even sold without necessity of any permission from the original author. The Japanese decision is arguably in agreement with the U. Copyright Office, which asserts that "copyright does not protect ideas, concepts, systems, or methods of doing something.
Dollar bill elephant, an example of moneygami. Kawasaki rose using the twist fold devised by Toshikazu Kawasaki. The calyx is made separately. Chinese Golden Venture swans. From Wikipedia, the free encyclopedia.
For other uses of the term, see Paper folding disambiguation. For other uses of Origami, see Origami disambiguation. Mathematics of paper folding. A challenging miniature version of a paper crane.
Two examples of modular origami. An example of origami bonsai. Retrieved January 1, Patsy Wang Iverson et al. The Practical Illustrated Encyclopaedia of Origami. Origami to Astonish and Amuse.
Retrieved July 20, Retrieved April 9, Origami Kit for Dummies. Retrieved 3 Sep United States Copyright Office. Retrieved 4 Sep Retrieved 14 March The Middle Ages in Popular Culture: Medievalism and Genre — Student Edition , , p.
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