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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]
Paper craft is a collection of crafts using paper or card as the primary artistic medium for the creation of two or three-dimensional objects. Paper and card stock lend themselves to a wide range of techniques and can be folded, curved, bent, cut, glued, molded, stitched, or layered. [1] Papermaking by hand is also a paper craft.
[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.
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 designs of their choice along the edges of the folded paper. When the paper is unfolded, a symmetrical design reveals itself.
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Origami (折り紙, Japanese pronunciation: or [oɾiꜜɡami], from ori meaning "folding", and kami meaning "paper" (kami changes to gami due to rendaku)) is the Japanese art of paper folding. In modern usage, the word "origami" is often used as an inclusive term for all folding practices, regardless of their culture of origin.
The paper is folded in front of itself. 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 ...