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Mathematics Of OrigamiThe art of origami has received a considerable amount of mathematical study. Fields of interest include a given origami model's flat-foldability (whether the model can be flattened without damaging it) and the use of origami folds to solve mathematical equations. Some classical construction problems of geometry--trisecting an arbitrary angle, or doubling the volume of an arbitrary cube--are proven to be unsolvable using straightedge and compass, but can be solved using only a few origami folds. Origami folds can be constructed to solve square roots and cube roots; fourth-degree polynomial equations can also be solved by origami folds. The full scope of origami-constructible algebraic numbers (e.g. whether it encompasses fifth or higher degree polynomial roots) remains unknown. The problem of rigid origami, treating the folds as hinges joining two flat, rigid surfaces such as sheet metal, has great practical importance. For example, the Miura map fold is a rigid fold that has been used to deploy large solar panel arrays for space satellites. Folding a flat model from a crease pattern has been proven by Marshall Bern and Barry Hayes to be NP complete. http://citeseer.ist.psu.edu/bern96complexity.html Huzita's axioms are one important contribution to this field of study. External links
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