The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability (whether the model can be flattened without damaging it), and the use of paper folds to solve up-to cubic mathematical equations.
Computational origami is a recent branch of computer science that is concerned with studying algorithms that solve paper-folding problems. The field of computational origami has also grown significantly since its inception in the 1990s with Robert Lang's TreeMaker algorithm to assist in the precise folding of bases. Computational origami results either address origami design or origami foldability. In origami design problems, the goal is to design an object that can be folded out of paper given a specific target configuration. In origami foldability problems, the goal is to fold something using the creases of an initial configuration. Results in origami design problems have been more accessible than in origami foldability problems.
History of origami
In 1893, Indian civil servant T. Sundara Row published Geometric Exercises in Paper Folding which used paper folding to demonstrate proofs of geometrical constructions. This work was inspired by the use of origami in the kindergarten system. Row demonstrated an approximate trisection of angles and implied construction of a cube root was impossible.
In 1922, Harry Houdini published "Houdini's Paper Magic," which described origami techniques that drew informally from mathematical approaches that were later formalized.
In 1936 Margharita P. Beloch showed that use of the 'Beloch fold', later used in the sixth of the Huzita–Hatori axioms, allowed the general cubic equation to be solved using origami.
In 1949, R C Yeates' book "Geometric Methods" described three allowed constructions corresponding to the first, second, and fifth of the Huzita–Hatori axioms.
The Yoshizawa–Randlett system of instruction by diagram was introduced in 1961.
In 1980 was reported a construction which enabled an angle to be trisected.
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Covers fundamental operations and constructibility in Euclidean geometry, exploring the limitations of geometric constructions and historical contributions.
A methodology for designing cylindrical origami with different patterns and different cross-sectional shapes is presented. Planar and cylindrical origami with curved-crease patterns are designed and proved to be foldable and developable regardless of the t ...
This work investigates the development of a Curved Origami Prototype made with timber panels. In the last fifteen years the timber industry has developed new, large size, timber panels. Composition and dimensions of these panels and the possibility of mill ...
A square trisection is a problem of assembling three identical squares from a larger square, using a minimal number of pieces. This paper presents an historical overview of the square trisection problem starting with its origins in the third century. We de ...