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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 ).
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.
Paper cutters were developed and patented in 1844 by French inventor Guillaume Massiquot. Later, Milton Bradley patented his own version of the paper cutter in 1879. [1] Since the middle of the 19th century, considerable improvements to the paper cutter have been made by Fomm and Krause of Germany, Furnival in England, and Oswego and Seybold in the United States.
Straight cut. There is one long tab. 1 ⁄ 3 cut. There are three tab positions, each is approximately 1 ⁄ 3 of the total length of the folder. Essentially, tabs are cut to be in the left, center, or right positions. 1 ⁄ 5 cut. Similar to the 1 ⁄ 3 cut, except there are five tab positions, each being 1 ⁄ 5 of the total length of the ...
Moving the handle pushes the head straight through the sheets of paper. The hard edge of the punch vs the die cuts a hole in the paper, pushing the cut piece out the bottom of the die. The cut-out bit of paper scrap is called a chad. The handle functions as a lever, decreasing the amount of force the operator needs to apply.
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