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The fold-and-cut theorem states that any shape with straight sides can be cut from a single (idealized) sheet of paper by folding it flat and making a single straight complete cut. [1] Such shapes include polygons, which may be concave, shapes with holes, and collections of such shapes (i.e. the regions need not be connected ).
An example of various paper snowflake designs. A paper snowflake is a type of paper craft based on a snowflake that combines origami with papercutting. The designs can vary significantly after doing mandatory folding. [1] An online version of the craft is known as "Make-A-Flake", and was created by Barkley Inc. in 2008. [2]
[28] [29] Snowflakes are also traditionally associated with the "White Christmas" weather that often occurs during Christmastide. [29] During this period, it is quite popular to make paper snowflakes by folding a piece of paper several times, cutting out a pattern with scissors and then unfolding it.
The book achieved enough success that the word kirigami was accepted as the Western name for the art of paper cutting. [1] Typically, kirigami starts with a folded base, which is then unfolded; cuts are then opened and flattened to make the finished design. Simple kirigami are usually symmetrical, such as snowflakes, pentagrams, or orchid blossoms.
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 a general Math Circle lesson, students use pattern finding, observation, and exploration to make their own mathematical discoveries. For example, mathematical beauty arises in a Math Circle activity on symmetry designed for 2nd and 3rd graders, where students create their own snowflakes by folding a square piece of paper and cutting out ...
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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 ...
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