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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).
For convex polygons one can cut off each vertex in turn, while for concave polygons this requires more care. A general approach that works for non-simple polygons as well would be to choose a line not parallel to any of the sides of the polygon and draw a line parallel to this one through each of the vertices of the polygon.
With a construction system that can trisect angles, such as mathematical origami, more numbers of sides are possible, using Pierpont primes in place of Fermat primes, including -gons for equal to 7, 13, 14, 17, 19, etc. [6] Geometric Origami provides explicit folding instructions for 15 different regular polygons, including those with 3, 5, 6 ...
Drawing tools such as ovals, freehand, polygon and text, with fill or shadow for polygons and closed freehand shapes. Cut and paste by selecting irregular regions or polygons. Preliminary print support using gnome-print. Modern, easy-to-use user interface with tool and color palettes. Multiple-image editing in a single instance of the program.
Referring to the image above, ABCM is an external boundary of a planar region with a hole FGHJ. The cut ED connects the hole with the exterior and is traversed twice in the resulting weakly simple polygonal representation. In an alternative and more general definition of weakly simple polygons, they are the limits of sequences of simple polygons.
The tattooed corpse of a woman was found bizarrely stuffed in a refrigerator dumped in some New Jersey woods — and cops say they need the public’s help identifying her.
Calories cut: 40 There's no doubt that chips make for an enjoyable, crunchy, salty snack, but a single serving can set you back nearly 150 calories . Instead, choose air-popped popcorn for a ...
The cut surface or vertex figure is thus a spherical polygon marked on this sphere. One advantage of this method is that the shape of the vertex figure is fixed (up to the scale of the sphere), whereas the method of intersecting with a plane can produce different shapes depending on the angle of the plane.