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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 ...
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.
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.
A guillotine-cut (also called an edge-to-edge cut) is a straight bisecting line going from one edge of an existing rectangle to the opposite edge, similarly to a paper guillotine. Guillotine cutting is particularly common in the glass industry. Glass sheets are scored along horizontal and vertical lines, and then broken along these lines to ...
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.
SFM is a combination of diameter and the velocity (RPM) of the material measured in feet-per-minute as the spindle of a milling machine or lathe. 1 SFM equals 0.00508 surface meter per second (meter per second, or m/s, is the SI unit of speed). The faster the spindle turns, and/or the larger the diameter, the higher the SFM.
Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible. Many of these problems can be related to real-life packaging, storage and ...