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Mathematics of paper folding. Map folding for a 2×2 grid of squares: there are eight different ways to fold such a map along its creases. The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability (whether the model can be flattened ...
Carpenter's rule problem. The carpenter's rule problem is a discrete geometry problem, which can be stated in the following manner: Can a simple planar polygon be moved continuously to a position where all its vertices are in convex position, so that the edge lengths and simplicity are preserved along the way? A closely related problem is to ...
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 ...
Huzita–Hatori axioms. The Huzita–Justin axioms or Huzita–Hatori axioms are a set of rules related to the mathematical principles of origami, describing the operations that can be made when folding a piece of paper. The axioms assume that the operations are completed on a plane (i.e. a perfect piece of paper), and that all folds are linear.
The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin can increase its perimeter. The problem is known under several names, including the Margulis napkin problem, suggesting it is due to Grigory Margulis, and the Arnold's rouble problem referring ...
The book is organized into three sections, on linkages, origami, and polyhedra. [1] [2]Topics in the section on linkages include the Peaucellier–Lipkin linkage for converting rotary motion into linear motion, [4] Kempe's universality theorem that any algebraic curve can be traced out by a linkage, [1] [4] the existence of linkages for angle trisection, [1] and the carpenter's rule problem on ...
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 ...
The term convolution refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The integral is evaluated for all values of shift, producing the convolution function.
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