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The map folding and stamp folding problems are related to a problem in the mathematics of origami of whether a square with a crease pattern can be folded to a flat figure. If a folding direction (either a mountain fold or a valley fold ) is assigned to each crease of a strip of stamps, it is possible to test whether the result can be folded ...
Unfold these two radial folds. Make another fold across the top connecting the ends of the creases to create a triangle of creases. Unfold this fold as well. Fold one layer of the open point upward and flatten it using the existing creases. A petal fold is equivalent to two side-by-side rabbit ears, which are connected along the reference crease.
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 ...
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. The Miura fold is a solution to the problem, and several others have been proposed. [43]
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Geometric Origami is a book on the mathematics of paper folding, focusing on the ability to simulate and extend classical straightedge and compass constructions using origami. It was written by Austrian mathematician Robert Geretschläger [ de ] and published by Arbelos Publishing (Shipley, UK) in 2008.
It includes the NP-completeness of testing flat foldability, [2] the problem of map folding (determining whether a pattern of mountain and valley folds forming a square grid can be folded flat), [2] [4] the work of Robert J. Lang using tree structures and circle packing to automate the design of origami folding patterns, [2] [4] the fold-and ...
Geometric Exercises in Paper Folding is a book on the mathematics of paper folding. It was written by Indian mathematician T. Sundara Row, first published in India in 1893, and later republished in many other editions. Its topics include paper constructions for regular polygons, symmetry, and algebraic curves. According to the historian of ...