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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 ...
In the early 1980s, Professor Chatani began to experiment with cutting and folding paper to make unique and interesting pop-up cards. He used the techniques of origami (Japanese paper folding) and kirigami (Japanese papercutting ), as well as his experience in architectural design, to create intricate patterns that played with light and shadow ...
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.
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]
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.
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 ...
Cartographic symbology encodes information on the map in ways intended to convey information to the map reader efficiently, taking into consideration the limited space on the map, models of human understanding through visual means, and the likely cultural background and education of the map reader. Symbology may be implicit, using universal ...
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 ...