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Fold-and-cut theorem. Creating a Koch snowflake curve by the fold-and-cut method. 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 ...
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.
Cutting stock problem. In operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted. It is an optimization problem in mathematics that arises from applications in industry.
Scherenschnitte (German pronunciation: [ˈʃeːʁənˌʃnɪtə]), which means "scissor cuts" in German, is the art of paper cutting design. The artwork often has rotational symmetry within the design, and common forms include silhouettes, valentines, and love letters. The art tradition was founded in Switzerland and Germany in the 16th century ...
Chinese paper cuttings (2014) Papercutting or paper cutting is the art of paper designs. Art has evolved all over the world to adapt to different cultural styles. One traditional distinction most styles share is that the designs are cut from a single sheet of paper as opposed to multiple adjoining sheets as in collage.
Kirigami. Kirigami (切り紙) is a variation of origami, the Japanese art of folding paper. In kirigami, the paper is cut as well as being folded, resulting in a three-dimensional design that stands away from the page. Kirigami typically does not use glue.
A hole punch, also known as hole puncher, or paper puncher, is an office tool that is used to create holes in sheets of paper, often for the purpose of collecting the sheets in a binder or folder (such collected sheets are called loose leaves). A hole punch can also refer to similar tools for other materials, such as leather, cloth, or sheets ...
Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex that may be folded to form a flat figure. It states that the pattern is flat-foldable if and only if alternatingly adding and subtracting the angles of consecutive folds around the vertex gives ...