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In 1996, Marshall Bern and Barry Hayes showed that the problem of assigning a crease pattern of mountain and valley folds in order to produce a flat origami structure starting from a flat sheet of paper is NP-complete. [18] In 1999, a theorem due to Haga provided constructions used to divide the side of a square into rational fractions. [19] [20]
However, the theorem remains valid in the Euclidean plane, with the correct interpretation of what happens when some opposite sides of the hexagon are parallel. If exactly one pair of opposite sides of the hexagon are parallel, then the conclusion of the theorem is that the "Pascal line" determined by the two points of intersection is parallel ...
Modular origami or unit origami is a multi-stage paper folding technique in which several, or sometimes many, sheets of paper are first folded into individual modules or units and then assembled into an integrated flat shape or three-dimensional structure, usually by inserting flaps into pockets created by the folding process. [3]
The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side. From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles.
The term "isometric" comes from the Greek for "equal measure", reflecting that the scale along each axis of the projection is the same (unlike some other forms of graphical projection). An isometric view of an object can be obtained by choosing the viewing direction such that the angles between the projections of the x , y , and z axes are all ...
The opposite side, figure 2, is decorated with purple, gray, and yellow. Note the different patterns used for the colors on the two sides. Figure 3 shows the first fold, and figure 4 the result of the first nine folds, which form a spiral.
The "recto" and "verso" terms can also be employed for the front and back of a one-sheet artwork, particularly in drawing. A recto-verso drawing is a sheet with drawings on both sides, for example in a sketchbook—although usually in these cases there is no obvious primary side. Some works are planned to exploit being on two sides of the same ...
Hex was also issued as one of the games in the 1974 3M Paper Games Series; the game contained a 5 + 1 ⁄ 2-by-8 + 1 ⁄ 2-inch (140 mm × 220 mm) 50-sheet pad of ruled Hex grids. Hex is currently published by Nestorgames in a 11×11 size, a 14×14, and a 19×19 size.