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In the stamp folding problem, the paper is a strip of stamps with creases between them, and the folds must lie on the creases. In the map folding problem, the paper is a map, divided by creases into rectangles, and the folds must again lie only along these creases. Lucas (1891) credits the invention of the stamp folding problem to Émile ...
A dashed and dotted line shows a mountain fold (there may be one or two dots per dash depending on the author). The paper is folded behind itself, this is normally done by turning the paper over, folding a valley fold and then turning the paper back over again. A thin line shows where a previous fold has creased the paper.
The fold-and-cut problem asks what shapes can be obtained by folding a piece of paper flat, and making a single straight complete cut. The solution, known as the fold-and-cut theorem, states that any shape with straight sides can be obtained. A practical problem is how to fold a map so that it may be manipulated with minimal effort or movements.
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.
Maekawa's theorem is a theorem in the mathematics of paper folding named after Jun Maekawa. It relates to flat-foldable origami crease patterns and states that at every vertex, the numbers of valley and mountain folds always differ by two in either direction. [1] The same result was also discovered by Jacques Justin [2] and, even earlier, by S ...
The Miura fold is a form of rigid origami, meaning that the fold can be carried out by a continuous motion in which, at each step, each parallelogram is completely flat. This property allows it to be used to fold surfaces made of rigid materials, making it distinct from the Kresling fold and Yoshimura fold which cannot be rigidly folded and ...
Hull is the author or co-author of several books on origami, including: Origametry: Mathematical Methods in Paper Folding (Cambridge University Press, 2021) [8]; Project Origami: Activities for Exploring Mathematics (AK Peters, 2006; 2nd ed., CRC Press, 2013) [9]
Geometric Folding Algorithms: Linkages, Origami, Polyhedra is a monograph on the mathematics and computational geometry of mechanical linkages, paper folding, and polyhedral nets, by Erik Demaine and Joseph O'Rourke. It was published in 2007 by Cambridge University Press (ISBN 978-0-521-85757-4).